Dynamics of a 3-UPS-UPU-S Parallel Mechanism
Abstract
:1. Introduction
2. A Novel 2-Rotational-DoF Parallel Mechanism () and Its DoF
2.1. Fundamentals of Screw Theory
2.2. Reciprocal Screws of Moving Platform and Its DOF
3. The Velocity and Displacement Analysis of the Parallel Mechanism
4. The Analysis of Acceleration and Its Mathematical Expression
5. The Analysis of Dynamics of the Parallel Mechanism
6. Simulation and Result Analysis
6.1. The Inverse Kinematics of the Parallel Mechanism
6.2. The Inverse Dynamics of the Parallel Mechanism
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Notation | Parameter |
Acceleration | |
Linear acceleration | |
Displacement coefficient matrix | |
Linear displacement | |
Displacement | |
Orientation vector | |
Force | |
Initial distance between base platform and middle ring of moving platform | |
3rd-order identity matrix | |
th joint | |
Moment of inertia of a single-rigid-body in the absolute coordinate frame | |
Matrix of mass moment of inertia of a single-rigid-body at its principal coordinate frame of the mass center | |
th kinematic chain in parallel mechanism | |
Initial length of kinematic chains | |
th link | |
Operation of Lie Brackets | |
Mass matrix | |
Number of iterations | |
th joint in one kinematic chain | |
Wrench vector consisting of constraint forces and torques | |
Radius of the middle ring of the moving platform | |
Position vector | |
Radius of circumcircle of four joints on the base platform | |
Rotation transformation matrix around axis | |
Screw matrix | |
Constraint space | |
Free motion space | |
Lie brackets of the unit screws | |
Inverse screw | |
Unit screw | |
Translation in direction | |
Torque | |
Linear velocity | |
Velocity screw | |
Coriolis wrench matrix | |
Angular velocity | |
Angular acceleration | |
Angular displacement |
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Mass | Moments of inertia |
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Zhao, J.-S.; Wei, S.-T.; Sun, X.-C. Dynamics of a 3-UPS-UPU-S Parallel Mechanism. Appl. Sci. 2023, 13, 3912. https://doi.org/10.3390/app13063912
Zhao J-S, Wei S-T, Sun X-C. Dynamics of a 3-UPS-UPU-S Parallel Mechanism. Applied Sciences. 2023; 13(6):3912. https://doi.org/10.3390/app13063912
Chicago/Turabian StyleZhao, Jing-Shan, Song-Tao Wei, and Xiao-Cheng Sun. 2023. "Dynamics of a 3-UPS-UPU-S Parallel Mechanism" Applied Sciences 13, no. 6: 3912. https://doi.org/10.3390/app13063912
APA StyleZhao, J.-S., Wei, S.-T., & Sun, X.-C. (2023). Dynamics of a 3-UPS-UPU-S Parallel Mechanism. Applied Sciences, 13(6), 3912. https://doi.org/10.3390/app13063912