Journal articles: 'FREEDOM BALL'

1

Alfares, Mohammed, Ghanim Al-Daihani, and Jasim Baroon. "The impact of vibration response due to rolling bearing components waviness on the performance of grinding machine spindle system." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 3 (April 10, 2019): 747–62. http://dx.doi.org/10.1177/1464419319838773.

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In this research, an analytical model based on a five-degrees-of-freedom nonlinear dynamical system was utilized to investigate the impact of vibration response due to inner race, outer race, and ball bearing waviness on the performance of grinding machine spindle system supported by two angular ball bearings. The waviness of rolling elements is modeled as a sinusoidal function is incorporated along the inner or outer races of bearing and ball surface. The elastic deflection and nonlinear contact force are calculated based on Hertzian contact model, while the shaft has five-degrees-of-freedom motions, three translational and two angular motions. The five–degrees-of-freedom nonlinear governing equations of the spindle system were developed taking into consideration the effect of outer race, inner race, and ball surface waviness, which are included in the kinematic constraints and force equilibrium equations of a ball. The developed model and its results are validated against results found in literature. Results by this paper indicate that the inner race waviness can significantly distort the tolerance and machining quality of grinding spindle-bearing systems more than does waviness in the outer race and ball elements. This is because the inner race waviness generates more complicated vibrations than the outer race and ball waviness. The most severe vibrations caused by the inner race waviness were found to occur when the waviness was of the order that is equal to multiple of number of balls in a bearing set plus or minus one ([Formula: see text]).

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2

Hore, J., S. Watts, and D. Tweed. "Arm position constraints when throwing in three dimensions." Journal of Neurophysiology 72, no. 3 (September 1, 1994): 1171–80. http://dx.doi.org/10.1152/jn.1994.72.3.1171.

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1. Overarm throwing is a skilled multijoint movement with potentially many degrees of freedom. Considering only the arm > or = 7 degrees of freedom are involved (shoulder 3, elbow 2, wrist 2). For each arm segment 3 degrees of freedom are potentially required to specify its angular position (orientation) at any moment during a throw. Simplification of the control problem for the CNS would occur if there were constraints on these degrees of freedom. The objective was to determine whether such constraints exist at ball release when throwing at targets in different directions using only the arm. 2. The angular positions in three dimensions of the distal phalanx of the middle finger, the hand, the forearm, and the upper arm were simultaneously recorded with search coils as subjects sat with a fixed trunk and threw balls at nine targets in an approximate +/- 40 degree work space. Ball release was signaled by microswitches on the proximal and distal phalanges of the middle finger (proximal and distal triggers). 3. On throwing at any one target the hand at ball release adopted a similar orientation for each throw, i.e., for a particular vertical and horizontal angular position the hand adopted a similar torsional position. On throwing at targets throughout the work space, angular position (rotation) vectors describing hand positions in space at ball release were confined to a two-dimensional surface rather than a three-dimensional volume. This constraint in hand torsion occurred near and at ball release but not throughout the entire throw. It was not due to mechanical factors because such a surface was not obtained when subjects deliberately twisted their arms when throwing. Thus at ball release during a "natural" throw the hand was constrained to 2 of its possible 3 angular degrees of freedom. 4. The same constraint was also found for finger, forearm, and upper arm angular positions in space at ball release as determined at both the proximal and distal triggers. A consequence is that at ball release the entire arm was constrained to 2 of its possible 7 degrees of freedom. 5. The two-dimensional position vector surface for each arm segment was similar to that obtained when pointing with a straight arm at the same targets. In both cases they showed torsion and were twisted like the surface obtained by rotations around the horizontal and vertical axes of a Fick gimbal. However, in some subjects the throwing surfaces were tilted from the vertical.(ABSTRACT TRUNCATED AT 400 WORDS)

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Geng, Keke, and Shengye Lin. "Effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 4 (November 7, 2019): 946–62. http://dx.doi.org/10.1177/0954406219885979.

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The double-row self-aligning ball bearing commonly runs with angular misalignment between the inner and outer rings, and the angular misalignment significantly affects the bearing performance. However, the effect of angular misalignment on the dynamic characteristics of the double-row self-aligning ball bearing has not been studied thoroughly. This paper investigates the effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing. The quasi-static model for the double-row self-aligning ball bearing is established with five degrees of freedom, namely, three translational displacements along x, y, and z directions and two tilting angles around x-axis and y-axis. The internal clearance between balls and raceways is included in the presented model. The formulation of the three-dimensional stiffness matrix for the double-row self-aligning ball bearing is analytically derived, and is verified by comparing with the available dada in published literature. Finally, the stiffness of the double-row self-aligning ball bearing under various angular misalignment conditions is analyzed systematically. The results show that the tilting angles vary the contact angles and contact forces of the compressed balls in the double-row self-aligning ball bearing, thus affect the bearing stiffness; the bearing stiffness decreases with the internal clearance; the angular misalignment significantly impacts the stiffness of the bearing running at a low speed.

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Meeks, Crawford R., and Long Tran. "Ball Bearing Dynamic Analysis Using Computer Methods—Part I: Analysis." Journal of Tribology 118, no. 1 (January 1, 1996): 52–58. http://dx.doi.org/10.1115/1.2837092.

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An analytical ball bearing dynamics model was developed that rigorously models all of the significant kinematic, structural, and dynamic effects. The model can analyze bearings of any material combination for the races, balls and ball cage. This model analyzes the stresses and deflections of the loaded elements due to (1) preload, (2) external axial, radial and moment loads, (3) centrifugal and gyroscopic ball loads. A rigorous six-degree-of-freedom model of ball cage motions was developed to analyze ball and cage dynamics. The ball cage equations of motion were written in a rotating coordinate system, which greatly simplifies the equations, resulting in a highly efficient, but rigorous, model of bearing dynamics. A computer program was developed, incorporating the algorithms, to solve the multiple simultaneous quasi-static ball-to-race load equations using modified Newton-Raphson methods. The Lawrence Livermore Ode package (LSODA) is employed for numerical integration of the dynamic equations of motion. This method assures convergence, while controlling the accuracy of the calculations as a function of computer run time and automatically selects the appropriate integration method for stiff and non-stiff system of ODE. The program analyzes ball and cage motions in time domain, wear life, fatigue life, lubricant film effects, ball-to-cage forces, torque noise and many other bearing parameters.

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Wang, L.-Q., L. Cui, L. Gu, and D.-Z. Zheng. "Study on dynamic characteristics of angular ball bearing with non-linear vibration of rotor system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 9 (September 1, 2008): 1811–19. http://dx.doi.org/10.1243/09544062jmes817.

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A rotor system supported by an angular ball bearing displays very complicated non-linear behaviour due to non-linear Hertzian contact force. The non-linear force and moment caused by the ball bearing are calculated on the basis of the relationship between deflection, and five-degree-of-freedom dynamic equations of the rotor ball bearing system are established. The Newmark-β method and the Newton—Raphson method are used to solve the non-linear equations. The dynamic characteristics of angular ball bearings are computed, considering the non-linear vibration of the rotor system. Taking angular ball bearing QJS208ACQ4C1/HNP4 as an example, the effects of the vibration of the rotor system on bearing dynamic characteristics are analysed. The results show that the spin-to-roll ratio of balls, the slide ratio of the cage, and stiffness of the bearing all vary obviously with the non-periodic vibration range of the rotor; initial contact angle and axial load of the ball bearing change the non-linear dynamic nature of the rotor system and dynamic characteristics of the bearing. The rotor ball bearing system can work stably by choosing the structural and operation parameters reasonably.

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Ma, Tianxiang, Shengqi Yang, Yongsen Xu, Dachuan Liu, Jinghua Hou, and Yunqing Liu. "Analysis and Correction of Measurement Error of Spherical Capacitive Sensor Caused by Assembly Error of the Inner Frame in the Aeronautical Optoelectronic Pod." Sensors 22, no. 23 (December 6, 2022): 9543. http://dx.doi.org/10.3390/s22239543.

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The ball joint is a multi-degree-of-freedom transmission pair, if it can replace the inner frame in the aviation photoelectric pod to carry the optical load, which will greatly simplify the system structure of the photoelectric pod and reduce the space occupied by the inner frame. However, installation errors in ball joint siting introduce nonlinear errors that are difficult to correct and two degree of freedom angular displacement of the ball joint is difficult to detect, which limits application in the precision control of two degrees of freedom systems. Studies of spherical capacitive sensors to date have not tested sensors for use in an inner frame stabilisation mechanism nor have they analysed the influence of installation error on sensor output. A two-axis angular experimental device was designed to measure the performance of a ball joint capacitive sensor in a frame stabilisation mechanism in an aeronautical optoelectronic pod, and a mathematical model to compensate for ball joint capacitive sensor installation error was created and tested. The experimental results show that the resolution of the capacitive sensor was 0.02° in the operating range ±4°, the repeatability factor was 0.86%, and the pulse response time was 39 μs. The designed capacitive sensor has a simple structure, high measurement accuracy, and strong robustness, and it can be integrated into ball joint applications in the frames of aeronautical photoelectric pods.

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MIYAZAKI, Tetsuro, and Kazushi SANADA. "Degrees of Freedom and Motion Design of Ball Throwing Robot Maximizing Ball Flying Distance." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2016 (2016): 2P2–04a6. http://dx.doi.org/10.1299/jsmermd.2016.2p2-04a6.

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Wu, Xibao, Wenbai Chen, and Weichen Li. "Realization of Humanoid Robot Playing Golf." Cybernetics and Information Technologies 16, no. 6 (December 1, 2016): 256–66. http://dx.doi.org/10.1515/cait-2016-0093.

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Abstract Aiming at the golf tournament technical requirements in International Humanoid robot Olympic Game (IHOG), two-freedom-degrees “head & eye” system based on monocular vision robot MF-AI is developed. The new robot equipped with the “head & eye” system can identify the location of the golf ball and the hole, and can measure the distance of the two objects. Experiments show that the two-freedom-degrees “head & eye” system improves the accuracy of hitting the golf ball into the hole. Moreover, the system can identify the target, can calibrate distances, can measure robot’s moving and look for the hole, can adjust the position of the robot and hit the ball effectively.

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Smagala, Arkadiusz, and Krzysztof Kecik. "Nonlinear Dynamics Analysis of a Rolling Bearing." Journal Européen des Systèmes Automatisés 54, no. 1 (February 28, 2021): 21–26. http://dx.doi.org/10.18280/jesa.540103.

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A numerical analysis of the nonlinear bearing model about two degrees of freedom has been presented in this paper. The contact between a ball and ring by Hertz theory is described. Influence of the number of balls, shaft rotation and clearance on the acceleration were investigated in detail. Three numbers of balls from 11 to 16 were analyzed. The clearance level in the range of 0-71μm has been studied. It has been shown that the acceleration responses are different, depending on the vibration direction and are usually higher when the radial internal clearance and the shaft speed are increased. The higher ball number caused that the accelerations decreased in both directions. Moreover, two dynamic indicators that can be used for comparison bearing dynamics have been proposed. These obtained results are useful for understanding the vibration response mechanism from a practical point of view.

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Liu, Chang, Chunyu Zhao, Zhendong Liu, and Shuai Wang. "Dynamic Analysis of Ball Screw Feed System with the Effects of Excitation Amplitude and Design Parameters." Applied Sciences 11, no. 15 (July 30, 2021): 7070. http://dx.doi.org/10.3390/app11157070.

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In this paper, a nine degree-of-freedom dynamic model of the ball screw feed system considering the contact nonlinearity between balls and raceways is established to analyze the vibration characteristics. The position relationship between raceway centers for the ball screw and bearings is determined by using the homogeneous coordinate transformation, and then the restoring force functions along the axial and lateral directions are derived. The dynamic equations of the feed system are solved by using Newmark method, and the proposed model is verified by the experimental method. Furthermore, the effect of the excitation amplitude on the axial vibration of the feed system is investigated by the frequency-amplitude curve and 3-D frequency spectrum. With the increase of excitation amplitude, the dynamic response of the feed system exits the softening, hardening type nonlinearity and jump phenomenon. Additionally, the effects of the initial contact angle, length of screw shaft and number of loaded balls on the axial vibration of the feed system in the resonance region are discussed. The results show that the dynamic model established in this paper is suitable for improving the machining accuracy and stability of the ball screw feed system.

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11

Cui, Li, and Qing Sheng Wang. "On the Bifurcation of Periodic Motion of Rotor Ball Bearing System Considering Five Degrees of Freedom." Advanced Materials Research 945-949 (June 2014): 707–10. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.707.

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Nonlinear bearing forces of ball bearing under five-dimensional loads are given, and five-DOF dynamic equations of rotor ball bearing system are constructed. Bifurcation of periodic motion of rotor ball bearing system in unbalance-rotating speed and radial clearance-rotating speed parametric domains are studied by use of continuation-shooting algorithm. Results show that the way of bifurcation and stability of period-1 motion vary with radial clearance and unbalance.

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12

Zhang, Penghai, Tao Wang, and Jun Zha. "A study on accuracy of linear ball guide." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 7 (February 16, 2022): 3293–312. http://dx.doi.org/10.1177/09544062211023069.

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The accuracy of linear motion guide greatly affects the form accuracy of the processed parts in precision machine tools. For the linear ball guide, it is an important issue that how to improve accuracy by optimizing structure parameters based on the geometric errors. Due to the diversity of geometric errors and structure parameters, it requires a quantitative indicator of error averaging ability to judge whether a linear ball guide has higher accuracy. In this article, based on the newly built accuracy model and the newly defined averaging coefficient, the influence of rail profile errors and deformation errors on the error motions in five degrees of freedom can be quantitatively studied for the guides with one row of balls, one block and four blocks. It finds that, both the straightness and angular accuracies increase as the number of contact balls increases. For the guides with one and four blocks, the profile errors with integer wave numbers have main influence on the straightness and primary angular (around the moving direction) error motions, while those near both sides of integer wave numbers have main influence on the supporting angular error motions. The influence of deformation errors on accuracy coincides with that of profile errors. The accuracy model discussed can be conveniently used to predict error motions, select optimized number of contact balls and select optimized spacing of adjacent mounting holes in the design process of linear ball guide.

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13

Jang, G. H., and S. W. Jeong. "Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid Rotor Supported by Two or More Ball Bearings Considering Five Degrees of Freedom." Journal of Tribology 124, no. 1 (June 1, 2001): 82–90. http://dx.doi.org/10.1115/1.1398289.

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This research presents a nonlinear model to analyze the ball bearing vibration due to the waviness in a rigid rotor supported by two or more ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by two or more ball bearings with waviness. It also characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing, and the sideband frequencies resulting from nonlinearity of the waviness interaction.

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Javorova, Juliana, and Anastas Ivanov. "Study of soccer ball flight trajectory." MATEC Web of Conferences 145 (2018): 01002. http://dx.doi.org/10.1051/matecconf/201814501002.

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In this paper the trajectories of a soccer ball for the most important kicks in the football game - a corner kick and a direct free kick are studied. The soccer ball is modelled as an ideal rigid hollow spherical body with six degrees of freedom, which performs a general motion in an immovable air environment with constant parameters. The ball 3D orientation is determined by the three Cardan angles. The aerodynamic forces and moments with which the air environment acts to the ball are taken into account. Two of the most dangerous areas of the football goal are defined. Differential equations which describe the motion of the soccer ball are solved numerically by MatLab-Simulink.

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Ngandu Kalala, Gauthier, Xavier Chiementin, Lanto Rasolofondraibe, Abir Boujelben, and Bovic Kilundu. "Modeling Impulsive Ball Mill Forces Effects on the Dynamic Behavior of a Single-Stage Gearbox." Machines 10, no. 4 (March 23, 2022): 226. http://dx.doi.org/10.3390/machines10040226.

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Gearboxes are frequently used in the mining industry, especially for power transmission between the electric drive and the ball mill; besides the extreme complexity of a ball mill gear transmission system, the fault diagnosis by vibration analysis can be easily distorted by the presence of impulsive noises due to the ball pulses on the mill shell. Although several works in the literature are related to the influence of an impulsive noise on the accuracy of the diagnosis, no dynamic model exists yet in the literature that can explain the influence of these forces on the dynamic behavior of gearboxes. This paper presents a new approach to determine the influence of the grinding forces in crack defects diagnosis. This approach is based on a hybrid numerical model of a 24-degree-of-freedom gearbox, simulating one gear train and two drive shafts. The impact forces of the mill drum are modelled by a discrete element method (DEM). The ball-filling rate (Fr), the mill speed (Nr), and the ball size (Db) are considered to study this phenomenon. The simulations results show by a time series representation, fast Fourier transform, and short-time Fourier transform (STFT), that the acceleration is significantly affected by the presence of the grinding forces, developing an impulsive noise due to the impact of the balls governed by the studied parameters.

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Rutci, Alimurtaza, and Fatih Selman Eren. "Investigation of Suspension Ball Joint Pull Out Force Based on FEA Method and Experimental Study." Academic Perspective Procedia 1, no. 1 (November 9, 2018): 1002–9. http://dx.doi.org/10.33793/acperpro.01.01.165.

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Suspension ball joints are always used to connect the control arms to the knuckle since they are the only joints which allow three degrees of rotational freedom. On the purpose of an sufficient performance of the ball joint, it is very important to prevent the extraction of the ball stud from the ball joint housing. Ball joint&rsquo;s housing material and shape design must withstand axial loads in the ball stud from axial direction in order to avoid the ball stud pull out keeping the ball stud inside the housing. The ball stud pull out force is a critical and safety characteristic function because it is related to failure mode for front suspension system. These paper investigate how to determine of suspension ball joint pull out force based on FEA method and experimental study. With respect to results of finite element analysis and experimental study, it is possible to monitoring deformation and displacement versus the load. The result of FE analysis and design verifications make it possible to determination of suspension ball joint pull out force.

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Hernot, X., M. Sartor, and J. Guillot. "Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach." Journal of Mechanical Design 122, no. 1 (January 1, 2000): 83–90. http://dx.doi.org/10.1115/1.533548.

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The stiffness matrix of angular contact ball bearings is calculated by using the analytical approach in which the summation of ball-race loads is replaced by an integration. The matrix connected to the conventional model in two degrees of freedom is first presented. A practical application of this formulation is illustrated through the common problem of sizing a two bearings-shaft arrangement. Variations of displacements, axial forces, and bearing fatigue life related to preload are shown to be easily obtained. Then, the matrix connected to the model in five degrees of freedom is given. This may be coupled with finite elements which are generally used to model the shaft or the housing. [S1050-0472(00)01801-8]

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Li, Yi Hao, and Wei Jiang. "Rigid Finite Element Modeling of Ball Screw System." Advanced Materials Research 538-541 (June 2012): 1006–10. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.1006.

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An integrated modeling method is proposed for ball screw drives which incorporates the elastic deformation of the screw within the nut. The ball screw model is derived based on Rigid Finite Element method, which is modeled as rigid multibody system consisting of rigid finite elements connected with spring damping elements, by using Rigid Finite Element method. The distributed contact stiffness of screw-nut interface is converted on ball screw and nut via Frenet-Serret coordinates. The proposed ball screw model has much less degrees of freedom than conventional finite element models. Comparisons between numerical simulations and experiments show that satisfied accuracy can also be obtained. The resulting model can be used for vibration analysis and control of ball screw drives.

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Kanga, Lusia Koja, Richardo Barry Astro, and Yasinta Embu Ika. "ANALYSIS OF VERTICAL MOVEMENTS ON FREEDOM AND BULLET MOVEMENT EVENTS USING VIDEO TRACKING METHOD." ScienceEdu 4, no. 1 (April 26, 2021): 19. http://dx.doi.org/10.19184/se.v4i1.23862.

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Analysis of vertical motion in free fall and bullet motion with the video tracking method has been carried out. This study aims to analyze the vertical motion pattern in the free fall and bullet motion, specifically the ball launching from the edge of the table. The research was carried out by rolling the ball until it slid and releasing the ball from the edge of the table until it experienced a free fall motion with the height of the table from the two activities of about 1 meter. This activity was carried out repeatedly until obtaining 5 videos of each event and recorded using the Vivo android camera. Furthermore, researchers analyzed using the Tracker application to obtain information data about vertical motion patterns, graphs of changes in position with time, and graphs of velocity against time. Result regressive analysis can derive equations Vy = Ax + B and Y = Ax + B

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Wang, Ming-Cheng, and Chung-Jen Lu. "Dynamic Characteristics of a One-Unit Ball-Rod-Spring Balancer." Journal of Vibration and Acoustics 129, no. 4 (April 16, 2007): 520–24. http://dx.doi.org/10.1115/1.2748462.

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The traditional ball-type automatic balancer consisting of several balls moving on a circular orbit is widely used in the optical disk drive industry for vibration reduction. Under proper working conditions, the balls can counterbalance the imbalance of a disk by positioning to appropriate angles relative to the mass center of the disk. This particular equilibrium position is referred to as the perfect balancing position. The proper working conditions are closely related to the stability of the perfect balancing position, which, in turn, depends on the parameters of the system, such as rotational speed, imbalance ratio, and damping ratios. To achieve perfect balancing, the system parameters must lie in the stable region of the perfect balancing position in the parameter space. An automatic balancer with a wider stable region can tolerate a larger amount of variations in the system parameters and hence is more robust. In this study, we propose a modified ball-type balancer composed of several ball-rod-spring units. In each unit, the ball can slide along the rod while the rod rotates freely about the spindle. The ball’s displacement along the rod is restrained by a radial spring. The additional degree of freedom in the radial direction could broaden the stable region of the perfect balancing position. To understand the fundamental properties of the modified balancer, we studied the dynamic characteristics of a modified balancer with one ball-rod-spring unit. Specifically, we built a theoretical model for an optical disk drive packed with the modified balancer, and investigated how equilibrium positions and the associated stability are related to primary system parameters and the effects of the stiffness of the radial spring on the stable region of the perfect balancing position. Numerical results indicate that the ball-rod-spring balancer may possess a larger stable region of the perfect balancing position compared to the traditional fixed-orbit balancer.

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Menh, Nguyen Cao. "On the technical diagnostics of ball-bearing based on modelling of rotor-bearing systems by vibration method." Vietnam Journal of Mechanics 29, no. 3 (September 22, 2007): 397–413. http://dx.doi.org/10.15625/0866-7136/29/3/5548.

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In this paper, after analysing deformations of loading ball-bearing it is able to investigate vibrations of rotor-bearing system as the system with non-linear and periodically varying stiffness. The modelling of the systems is depent on properties of the shaft (rigid or flexible) and on measurement techniques for system vibrations (by eddy current proximity probe for rotating shaft or on non-rotating parts of the rotor-bearing systems) it can be described by a single degree-of-freedom or two-degree-of freedom nonlinear systems subjected to parametric and external excitations. Therefore it is possible to obtain different characteristics of system vibrations with respect to different defects of ball-bearing. These symptoms help us to identify and estimate the bearing quality by measurement and analysis of system vibrations.

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Guseltseva, Marina. "Ratiohumanistic approach of H.O. Ball: psychology of freedom and creative synthesis." PSIHOLOGÌÂ Ì SUSPÌLʹSTVO 68, no. 2 (June 1, 2017): 41–55. http://dx.doi.org/10.35774/pis2017.02.041.

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Aziz, N. N. Abdul, M. I. Yusoff, M. I. Solihin, and R. Akmeliawati. "Two degrees of freedom control of a ball and beam system." IOP Conference Series: Materials Science and Engineering 53 (December 20, 2013): 012070. http://dx.doi.org/10.1088/1757-899x/53/1/012070.

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Aini, R., H. Rahnejat, and R. Gohar. "Vibration Modeling of Rotating Spindles Supported by Lubricated Bearings." Journal of Tribology 124, no. 1 (August 29, 2000): 158–65. http://dx.doi.org/10.1115/1.1332398.

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This paper outlines a five degrees of freedom model of a rotating spindle supported by a pair of lubricated angular contact ball bearings. The ball to raceway contacts are simulated by non-linear contact springs, representing the elastic deformation of the mating rolling members and nonlinear spring/dampers, corresponding to the contact elastohydrodynamic oil film thickness. A regression formula is used to model the latter and includes the damping contributed by the squeeze film effect caused by the mutual convergence of bearing rings. Some results of simulation studies with the model are also presented, in both the time and frequency domains. They include the overall system response, when subjected to varying spindle mass or the number of balls in the support bearings. Furthermore, comparisons are made between the simulated response of the dry and lubricated models. The overall contribution to damping of the elastohydrodynamic oil films between the rolling elements and their raceways is shown to be slight.

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Ren, Sheng-Le, and Ming-Yuan Ren. "Damping analysis of micro-gyroscope with ball-disk rotor." AIP Advances 12, no. 8 (August 1, 2022): 085011. http://dx.doi.org/10.1063/5.0101941.

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According to the structure of the micro-gyroscope with a ball-disk rotor, the corresponding Reynolds equation is solved by using the motion equation, continuity equation, and state equation. The damping coefficients of axial vibration, radial vibration, and rotation around the Z axis are derived theoretically. The damping theoretical model of the micro-gyroscope is constructed to analyze the gas film damping and oil film damping of the ball-disk rotor in three degrees of freedom motion.

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Lee, Dong-Soo, and Dong-Hoon Choi. "A Dynamic Analysis of a Flexible Rotor in Ball Bearings with Nonlinear Stiffness Characteristics." International Journal of Rotating Machinery 3, no. 2 (1997): 73–80. http://dx.doi.org/10.1155/s1023621x97000080.

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This paper presents an effective analysis approach for a flexible rotor in ball bearings with nonlinear stiffness characteristics to obtain realistic dynamic behavior results. The ball bearing is modeled in five degrees of freedom and the nonlinear stiffness characteristics of the bearing are completely described as functions of combined loads and spin speed. For dynamic behavior analysis of the nonlinear rotor-bearing system, a transfer-matrix method is iteratively used until the bearing displacements and the shaft displacements at every bearing location converge to the same values. The results show that the nonlinear stiffness characteristics of ball bearings significantly influence system dynamic behaviors and the proposed analysis approach for the nonlinear rotor-bearing system is effective.

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W Thaldar, Donrich, and Michaela Steytler. "Time for Cinderella to go to the ball: Reflections on the right to freedom of scientific research." South African Law Journal 138, no. 2 (2021): 260–88. http://dx.doi.org/10.47348/salj/v138/i2a2.

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Despite the fact that the Constitution explicitly protects the right to freedom of scientific research, this right features neither in the preamble to any legislation, nor in any reported case law. If the right to freedom of scientific research remains in obscurity, South Africa could slip into totalitarian control of the scientific enterprise, to the detriment not only of scientists, but also of society in general. The right to freedom of scientific research should play a more central role in policy-making. This is not only because it is an enumerated constitutional right, but also because it is important in its own right, as it serves purposes that are at the core of our constitutional value-system: promoting individual autonomy, facilitating the search for truth, and supporting democracy. The right to freedom of scientific research is unique in protecting not only the exchange of scientific thoughts and information, but also in particular the physical activities entailed by scientific research, such as performing experiments. The notion that government should somehow seek to regulate every new scientific development is erroneous, as freedom should be the default position in science-related policy, and should only be limited by regulation if, and to the extent that, it is constitutionally justified.

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Iacob, Radu, Emil Budescu, Eugen Merticaru, and Cezar Oprişan. "The Kinematic Model with Three Degrees of Freedom Associated to the Direct Throwing in Basketball Game." Applied Mechanics and Materials 658 (October 2014): 495–500. http://dx.doi.org/10.4028/www.scientific.net/amm.658.495.

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The paper presents a reverse kinematic analysis for the free through to basket in order to determine the possible angular movement speed of the arm segments during throw flexion. The body segments offering three freedom degrees to the kinematic model are: the arm, the forearm and the hand. From geometric conditions regarding to the possibility of the ball to get through the basket and the analysis of the parabolic trajectory of the ball, one could determine the mathematical relations for the limitative values of the horizontal and vertical components of the initial velocity and consequently, for the calculation of the initial angle of throwing the ball. On the other hand, from the expression of the flexion movement of the considered body segments, it could be possible to obtain the calculation of the initial throw velocity as functions of the anthropometric data of the analyzed subject, of flexion angles and angular velocity of movement of the body segments. Using some models of functional mathematic analysis, from the two equations with three unknowns, one could determine the variation field of the system solutions. By setting the conditions related to the numeric limits of variation for the angular speed, the numeric field of the possible solutions for the equation system is straitened.

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Sun, Tao, Wen Wang, Zhanfeng Chen, Yewen Zhu, Kaifei Xu, Haimei Wu, Zhiqian Sang, Keqing Lu, and He Yang. "Positioning Errors Measurement of CNC Machine Tools Based on J-DBB Method." Applied Sciences 11, no. 24 (December 10, 2021): 11770. http://dx.doi.org/10.3390/app112411770.

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Due to the errors of the servo system and the errors of the ball screw drive system, the positioning errors inevitably occur in the process of CNC machine tools. The measurement of traditional equipment is limited by a fixed measurement radius and a single degree of freedom, which can only be measured within a fixed plane. In this paper, four different positioning errors of CNC machine tools are first measured at full scale by using J-DBB (a modified double ball bar with one spherical joint connecting two bars) method. The J-DBB device uses a three-degree-of-freedom spherical joint as a connecting part, which realizes that the measurement radius can be continuously changed, and the measurement space is a spatial sphere. First, the principle of the J-DBB method is briefly introduced. Next, four typical positioning errors of CNC machine tools are analyzed and examined, which contain the uniform contraction error of ball screw and linear grating, periodic error of the ball screw and linear grating, interference of measurement devices error, and opposite clearance error. In the end, the trajectories of the CNC machine tool spindle with a single positioning error are simulated by using the J-DBB method. The results reveal that this method can be used for the positioning error of machine tools, which helps to better understand the spatial distribution of CNC machine tool errors and provides guidance for the reasonable selection of working areas to improve the machining accuracy of parts.

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Choi, Y. H., S. M. Cha, J. H. Hong, and Jai Hyuk Choi. "A Study on the Vibration Analysis of a Ball Screw Feed Drive System." Materials Science Forum 471-472 (December 2004): 149–54. http://dx.doi.org/10.4028/www.scientific.net/msf.471-472.149.

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Feed drive system of machine tools may experience serious vibrations or unstable motions during high-speed operation. In this paper, a 6 D.O.F (Degree-Of-Freedom) lumped parameter model was proposed in order to analyze vibrations of a ball screw feed-drive system, which takes planar motion. The equations of motion were derived for the proposed model. Natural frequencies of the system and transient responses due to driving motor speed control input were also analyzed. Experimental modal analysis and operational vibration measurements of a laboratory ball screw feed drive system were made. Both theoretical analysis and experimental measurement results showed good agreement with each other. Consequently we concluded that the proposed 6 D.O.F model could be well applicable to the vibration analysis of a ball screw feed-drive system.

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Liu, Hua, Weidong Zhu, Huiyue Dong, and Yinglin Ke. "An adaptive ball-head positioning visual servoing method for aircraft digital assembly." Assembly Automation 39, no. 2 (April 1, 2019): 287–96. http://dx.doi.org/10.1108/aa-05-2018-066.

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PurposeTo gain accurate support for large aircraft structures by ball joints in aircraft digital assembly, this paper aims to propose a novel approach based on visual servoing such that the positioner’s ball-socket can automatically and adaptively approach the ball-head fixed on the aircraft structures.Design/methodology/approachImage moments of circular marker labeled on the ball-head are selected as visual features to control the three translational degrees of freedom (DOFs) of the positioner, where the composite Jacobian matrix is full rank. Kalman–Bucy filter is adopted for its online estimation, which makes the control scheme more flexible without system calibration. A combination of proportional control with sliding mode control is proposed to improve the system stability and compensate uncertainties of the system.FindingsThe ball-socket can accurately and smoothly reach its desired position in a finite time (50s). Positional deviations between the spherical centers of ball-head and ball-socket in theX-Yplane can be controlled within 0.05 mm which meets the design requirement.Practical implicationsThe proposed approach has been integrated into the pose alignment system. It has shown great potential to be widely applied in the leading support for large aircraft structures in aircraft digital assembly.Originality/valueAn adaptive approach for accurate support of large aircraft structures is proposed, which possesses characteristics of high precision, high efficiency and excellent stability.

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Shaikh, Samir, and Sham Kulkarni. "A theoretical model for predicting the vibration response of outer race defective ball bearing." International Journal of Engineering & Technology 7, no. 2 (March 13, 2018): 289. http://dx.doi.org/10.14419/ijet.v7i2.8953.

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The theoretical model with 2 degree-of-freedom system is developed for predicting the vibration response and analyze frequency properties in an extended type defective ball bearing. In the mathematical formulation, the contact between the races and rolling element considered as non-linear springs. The contact forces produced during the collaboration of rolling elements are obtained by utilizing Hertzian contact deformation hypothesis. The second order nonlinear differential equation of motion is solved using a state space variable method with the help of MATLAB software and the vibration acceleration response of the defective ball bearing presented in the frequency spectrum. The effects of variation in speed and size of the defect on characteristic frequency of extended fault on the outer raceway of the ball bearing have been investigated. The theoretical results of the healthy (non defective) and defective bearing are compared with each other.

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33

Hou, Pingping, Liqin Wang, and Qiuyang Peng. "Influence of rotational speed on the impact characteristics caused by a localized defect of the outer raceway in a ball bearing under an axial load." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 3 (May 21, 2020): 498–513. http://dx.doi.org/10.1177/1464419320923540.

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The rotational speed is a crucial parameter for bearing condition monitor. The present study shows the influence of the rotational speed on the impact characteristics caused by a localized defect of the outer raceway. A 2 Nb + 5-degrees-of-freedom nonlinear dynamic model for a ball bearing is developed. The waviness of bearing components, a localized defect of the outer raceway, and the centrifugal forces of balls caused by rotational speed are involved in the ball bearing model. Spectral kurtosis (SK) analysis and envelope spectrum analysis are used to extract the impact signal and confirm the position of the optimal frequency band affected by the impact signal. The peak of the impact signal rises with the increase in rotational speed. The position of the optimal frequency band affected by the impact signal is a linear piecewise function of the rotational speed. These simulated results are verified through vibration experiments of a ball bearing with a localized defect of the outer raceway under an axial load. In addition, considering both a localized defect on the outer raceway and the waviness of bearing components, only when the size of the localized defect is large enough, can the impact signal overcome the influence of the structural vibration of the system to extract impact characteristics. The case studies of high-speed spindle bearing state diagnosis show that high speed is not conducive to the extraction of the impact characteristics.

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Swanson, P. J., R. R. Burridge, and D. E. Koditschek. "Global asymptotic stability of a passive juggling strategy: A possible parts-feeding method." Mathematical Problems in Engineering 1, no. 3 (1995): 193–224. http://dx.doi.org/10.1155/s1024123x95000135.

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In this paper we demonstrate that a passive vibration strategy can bring a one-degree-of-freedom ball to a specified periodic trajectory from all initial conditions. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analysis to the parts feeding problem.

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Choi, Young Hyu, Sung Hyun Jang, and Ji Han Oh. "Influencing Factors on Stick-Slip Behavior of a Ball Screw Driven Elevation Mechanism for MLRS." Applied Mechanics and Materials 271-272 (December 2012): 958–68. http://dx.doi.org/10.4028/www.scientific.net/amm.271-272.958.

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As an MLRS (Multiple Launch Rocket System) cage is moved with a uniform speed through an elevation mechanism for MRLS operated using ball screws, its stick-slip behavior can be observed by the friction in a ball screw actuator. In this study, a single-degree of freedom mathematical model of an MLRS elevation system is designed and its stick-slip behavior is analyzed using a friction force model considering the Stribeck effect. The stability of a vibration system is analyzed through deriving an equation of normalized motion for the mathematical model and the influences of mechanical parameters and friction parameters on the vibration response and stability are theoretically analyzed.

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HAMAMATSU, Hiroshi, Kohtaro KOYAMA, Yoshito TANAKA, Shigeru FUTAMI, and Teruo TSUJI. "702 Design of Two-degree-of Freedom Control for Ball Screw Driving Mechanism." Proceedings of Conference of Kyushu Branch 2005.58 (2005): 243–44. http://dx.doi.org/10.1299/jsmekyushu.2005.58.243.

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37

Utley, Andrea, Bert Steenbergen, and Sarah Louise Astill. "Ball catching in children with developmental coordination disorder: control of degrees of freedom." Developmental Medicine & Child Neurology 49, no. 1 (December 21, 2006): 34–38. http://dx.doi.org/10.1017/s0012162207000096.x.

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38

Lichtenstein, Alex. "Ball and chain: An International Conference Exploring the Boundaries of Freedom and Coercion." International Labor and Working-Class History 52 (1997): 134–37. http://dx.doi.org/10.1017/s0147547900006979.

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39

Wu, Zhongke, Mingquan Zhou, and Xingce Wang. "Interactive Modeling of 3D Tree with Ball B-Spline Curves." International Journal of Virtual Reality 8, no. 2 (January 1, 2009): 101–7. http://dx.doi.org/10.20870/ijvr.2009.8.2.2731.

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A novel approach to modeling realistic tree easily through interactive methods based on ball B-Spline Curves (BBSCs) and an efficient graph based data structure of tree model is proposed in the paper. As BBSCs are flexible for modifying, deforming and editing, these methods provide intuitive interaction and more freedom for users to model trees. If conjuncted with other methods like generating tree models through L-systems or iterated function systems (IFS), the models are more realistic and natural through modifying and editing. The method can be applied to the design of bonsai tree models.

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Megasari, Anis Laela, and Rizka Adela Fatsena. "Application of SEFTnobirthing-Ball To The Progress of Childbirth Process In Maternity Mother Primigravida In BPM Ika Siswiyanti Demak City." Journal of Midwifery Science: Basic and Applied Research 3, no. 2 (December 16, 2021): 69–73. http://dx.doi.org/10.31983/jomisbar.v3i2.8116.

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Background: The maternal mortality rate in Indonesia is 38 thousand every day. One of the causes of the high mortality rate in Indonesia is prolonged labor. Prolonged labor is a labor process that lasts more than 24 hours in primiparas. There were 29 cases of old labor at the Independent Midwife Practice Ika Siswiyanti in Demak City in 2020, there were 29 cases, and all of these cases were referred. Self-birthing-ball is a combination of Spiritual Emotional Freedom Technique intervention with birthing ball that can reduce pain intensity and speed up the duration of labor. This study aims to determine the effect of self-birthing-ball on the progress of the first stage of labor in primigravida mothers. Methods: The design of this study was a Quasy experimental with a post-test only design. The research sample was 16 respondents obtained through purposive sampling, namely prospective respondents must meet the inclusion and exclusion criteria that have been determined. Statistical tests using Wilcoxon test. Results: The average percentage of labor progress is 3.2. statistical results obtained a p-value 0.031 (0.05), which shows that there has been an effect SEFTnobirthing-ball on the progress of the first stage of labor in primigravida mothers. Conclusion: SEFTnobirthing-ball proven to increase the progress of the first stage labor. Keywords: Birthing-ball; labor progress; first stage labor; SEFT

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41

Dong, Yanfang, Feifan Chen, Ming Qiu, Huijie Wang, and Chuanmeng Yang. "Study of the Contact Characteristics of Machine Tool Spindle Bearings under Strong Asymmetric Loads and High-Temperature Lubrication Oil." Lubricants 10, no. 10 (October 18, 2022): 264. http://dx.doi.org/10.3390/lubricants10100264.

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The contact characteristics of angular contact ball bearings are closely related to the thermal failure of high-speed spindle systems. This paper establishes a closed-loop iterative model for analyzing the ball–race contact characteristics of machine tool spindle bearings at different combined loads and oil supply temperatures, based on a five-degree-of-freedom quasi-static analysis model and the finite difference method. Additionally, the accuracy of the proposed model is verified by comparing the measured values of temperature rise with the predicted values. Based on the verification of the accuracy of the model, the contact characteristics of machine tool spindle bearings under strong asymmetric loads and high-temperature lubrication oil are discussed in detail. The results show that at elevated temperatures, the internal loads of angular contact ball bearings operating under combined loads become concentrated, which will lead to reduced fatigue life of the bearings and even thermal seizure.

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42

Guo, Jin, Jin-Huat Low, Jun Liu, Yangfan Li, Zhuangjian Liu, and Chen-Hua Yeow. "Three-Dimensional Printable Ball Joints with Variable Stiffness for Robotic Applications Based on Soft Pneumatic Elastomer Actuators." Polymers 14, no. 17 (August 29, 2022): 3542. http://dx.doi.org/10.3390/polym14173542.

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This paper contributes to a new design of the three-dimensional printable robotic ball joints capable of creating the controllable stiffness linkage between two robot links through pneumatic actuation. The variable stiffness ball joint consists of a soft pneumatic elastomer actuator, a support platform, an inner ball and a socket. The ball joint structure, including the inner ball and the socket, is three-dimensionally printed using polyamide−12 (PA12) by selective laser sintering (SLS) technology as an integral mechanism without the requirement of assembly. The SLS technology can make the ball joint have the advantages of low weight, simple structure, easy to miniaturize and good MRI compatibility. The support platform is designed as a friction-based braking component to increase the stiffness of the ball joint while withstanding the external loads. The soft pneumatic elastomer actuator is responsible for providing the pushing force for the support platform, thereby modulating the frictional force between the inner ball, the socket and the support platform. The most remarkable feature of the proposed variable stiffness design is that the ball joint has ‘zero’ stiffness when no pressurized air is supplied. In the natural state, the inner ball can be freely rotated and twist inside the socket. The proposed ball joint can be quickly stiffened to lock the current position and orientation of the inner ball relative to the socket when the pressurized air is supplied to the soft pneumatic elastomer actuator. The relationship between the stiffness of the ball joint and the input air pressure is investigated in both rotating and twisting directions. The finite element analysis is conducted to optimize the design of the support platform. The stiffness tests are conducted, demonstrating that a significant stiffness enhancement, up to approximately 508.11 N·mm reaction torque in the rotational direction and 571.93 N·mm reaction torque in the twisting direction at the pressure of 400 kPa, can be obtained. Multiple ball joints can be easily assembled to form a variable stiffness structure, in which each ball joint has a relative position and an independent stiffness. Additionally, the degrees of freedom (DOF) of the ball joint can be readily restricted to build the single-DOF or two-DOFs variable stiffness joints for different robotic applications.

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Wu, Shi, D. K. Jia, X. L. Liu, Y. C. Jiang, and Y. F. Li. "Research of Cutter Geometric Parameter Effect on Machining Stability Area in High Speed Milling Process." Advanced Materials Research 188 (March 2011): 150–53. http://dx.doi.org/10.4028/www.scientific.net/amr.188.150.

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In this paper, modal analysis of ball end mills is modeled by finite element to work out natural frequency and chatter model in tooling system and to calculate the limit curve of stability in single degree freedom system. The effect of cutter flute length and cutter tooth number on limit curve of stability in single degree freedom system is also discussed. The research results show that steady critical cutting depth of milling system declines while the cutter flute length increases, but the trend is not linear, which shows increase partly. An engineering optimization design is made on milling cutter geometrical parameters based on this conclusion.

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Choi, Kee-Bong, Jaejong Lee, Geehong Kim, Hyungjun Lim, and Soongeun Kwon. "Kinematic Analysis of a Parallel Manipulator Driven by Perpendicular Linear Actuators." Actuators 10, no. 10 (October 9, 2021): 262. http://dx.doi.org/10.3390/act10100262.

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In this paper, a goniometer-type specimen stage with a linear actuation mechanism mounted on a rotation mechanism is introduced. The linear actuation mechanism was modeled as a spatial parallel manipulator consisting of a moving body, three linear actuators, and an anti-rotation mechanism. The three linear actuators were arranged perpendicular to each other. In the specimen stage, the linear actuators were in ball contact with the surface of a holder designed to hold a specimen. For the parallel manipulator, the ball contact was replaced with two prismatic joints and a spherical joint. The mobility of the manipulator without the anti-rotation mechanism was one degree of freedom greater than the number of actuators. Therefore, the redundant one degree-of-freedom motion was restrained using an anti-rotation mechanism with three rotation joints and two prismatic joints. The inverse and direct kinematics of the goniometer mechanism were derived and verified. In addition, the inverse Jacobian was derived, and local and global performance indices were analyzed by the terms of manipulability and isotropy. Finally, the goniometer-type specimen stage was designed by the global performance indices.

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45

Spacek, Lubos, Jiri Vojtesek, and Frantisek Gazdos. "Control of Unstable Systems Using a 7 DoF Robotic Manipulator." Machines 10, no. 12 (December 5, 2022): 1164. http://dx.doi.org/10.3390/machines10121164.

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Robotic manipulators are widely used in industrial applications, and their rigidity and flexibility are very important factors during their deployment. However, their usage is not limited to repetitive point-to-point tasks and can be used for more real-time control of various processes. This paper uses a 7-degrees-of-freedom manipulator to control an unstable system (Ball and Plate) as a proof of concept. The Ball and Plate system is widely used for testing algorithms designed for unstable systems, and many recent works have dealt with robotic manipulators as a control motion system. Robots are not usually used to control unstable systems, but bipedal robots are an exception. This paper aims to design a controller capable of stabilizing an unstable system with solid robustness while keeping actuator action values as low as possible because these robots will be indented to work for a prolonged time. An algorithm for an LQ polynomial controller is described and designed, and the whole setup is tested for ball stabilization in the center. The results show that the designed controller stabilizes the ball even with large external and internal disturbances while keeping the controller effort as low as possible.

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46

Ambrożkiewicz, Bartłomiej, Grzegorz Litak, Anthimos Georgiadis, Nicolas Meier, and Alexander Gassner. "Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model." Applied Sciences 11, no. 2 (January 15, 2021): 787. http://dx.doi.org/10.3390/app11020787.

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Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

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Yun, Cheol-Ho, Shinichiro Niwano, James R. Friend, Kentaro Nakamura, and Sadayuki Ueha. "Support Mechanism for the Ball Rotor in the Three-Degree-of-Freedom Ultrasonic Motor." Japanese Journal of Applied Physics 42, Part 1, No. 5B (May 30, 2003): 3000–3001. http://dx.doi.org/10.1143/jjap.42.3000.

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MORI, Ibuki, Takaaki OIWA, Kenji TERABAYASHI, and Junichi ASAMA. "Kinematic calibration for three-degree-of-freedom parallel manipulator based on 3D-ball plate." Proceedings of Conference of Tokai Branch 2017.66 (2017): 216. http://dx.doi.org/10.1299/jsmetokai.2017.66.216.

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Mehedi, Ibrahim Mustafa, Ubaid M. Al-Saggaf, Rachid Mansouri, and Maamar Bettayeb. "Two degrees of freedom fractional controller design: Application to the ball and beam system." Measurement 135 (March 2019): 13–22. http://dx.doi.org/10.1016/j.measurement.2018.11.021.

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Ansoategui, Igor, and Francisco J. Campa. "Mechatronics of a ball screw drive using an N degrees of freedom dynamic model." International Journal of Advanced Manufacturing Technology 93, no. 1-4 (June 12, 2017): 1307–18. http://dx.doi.org/10.1007/s00170-017-0597-2.

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Journal articles on the topic 'FREEDOM BALL'

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