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RESEARCH PAPERS

A Unified Approach to Solving Driving Forces in Spatial Parallel Manipulators With Less Than Six DOFs

Yi Lu and Bo Hu
[+] Author and Article Information
Yi Lu

School of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004 Chinaluyi@ysu.edu.cn

Bo Hu

School of Mechanical Engineering, Yanshan University, Qinhuangdao, Hebei 066004 China

J. Mech. Des 129(11), 1153-1160 (Nov 03, 2006) (8 pages) doi:10.1115/1.2771237 History: Received March 22, 2006; Revised November 03, 2006

A unified approach to solving driving forces in spatial parallel manipulators with less than six DOFs is proposed. First, the geometric constrained equations of the parallel manipulators are derived, and some independent pose parameters and a common transformation matrix with three translations and three Euler rotations are determined. Second, the common formulas for solving inverse kinematics, the Jacobian matrix, and velocity are derived. Third, a common virtual serial mechanism with three virtual prismatic joints and three virtual revolute joints corresponding to three Euler rotations is constructed. Fourth, a common analytic formula for solving driving forces in spatial parallel manipulators with less than six DOFs is derived by using the principle of virtual work and the virtual serial mechanism. Finally, a 3-SPR parallel manipulator with three DOFs and a 4SPS+SPR parallel manipulator with five DOFs are presented to illustrate the use of the unified approach to solve their inverse kinematics and the driving forces. The solving results are verified by the simulation mechanisms.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A parallel manipulator with n linear driving limbs and its virtual serial mechanism

Grahic Jump Location
Figure 2

The 3-SPR parallel manipulator

Grahic Jump Location
Figure 3

The virtual serial mechanism of 3-SPR parallel manipulator

Grahic Jump Location
Figure 4

The 4SPS+SPR parallel manipulator and its virtual serial mechanism

Grahic Jump Location
Figure 5

The extension, two velocity, and driving forces versus time of ri for 3-SPR parallel manipulator

Grahic Jump Location
Figure 6

The extension, velocity, and driving forces versus time of ri for the 4SPS+SPR parallel manipulator

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