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Research Papers

Accurate Simulation Solutions of Euler Angular Velocity/Acceleration and Statics of Parallel Manipulators by CAD Variation Geometry

[+] Author and Article Information
Yi Lu

Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinaluyi@ysu.edu.cn

Jiayin Xu

Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinaxujiayin@ysu.edu.cn

JianPing Yu

College of Foreign Studies, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinayjp@ysu.edu.cn

Bo Hu

Robotics Research Center, College of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei, 066004, P. R. Chinahbz0001@yahoo.com.cn

J. Mechanisms Robotics 1(3), 031001 (May 12, 2009) (8 pages) doi:10.1115/1.3111265 History: Received January 17, 2008; Revised October 07, 2008; Published May 12, 2009

A CAD variation geometry approach is proposed for accurately solving the Euler angles, Euler angular velocity/acceleration, and the active forces due to a concentrated torque of limited-DOF parallel manipulators (PMs). First, a simulation mechanism of PM with Euler angles, a simulation mechanism of PM with Euler angular velocity/acceleration, and a simulation mechanism of PM with Euler angular torques are created and combined into one simulation mechanism. Second, when modifying the driving dimension of the active legs, the simulation mechanism of PM is varied correspondingly, and the Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved automatically and visualized dynamically. Third, a 3DOF PM and a 5DOF PM are illustrated, and their Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved accurately by CAD variation geometry and are verified by the analytic solutions.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A general simulation mechanism of PM with three Euler angles in rotation order of ZYX at three positions

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Figure 2

(a) 3SPR PM, (b) its simulation mechanism, (c) Euler angular velocities and their composite velocity versus δt=1, and (d) Euler angular accelerations and their composite acceleration versus δt=1

Grahic Jump Location
Figure 3

(a) A 4UPS+SPR PM and its simulation mechanism with Euler angular torques and active forces corresponding to (b) δr=10 cm and (c) δr=0.01 cm

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