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RESEARCH PAPERS

# Using CAD Variation Geometry and Analytic Approach for Solving Kinematics of a Novel 3-SPU/3-SPU Parallel Manipulator

[+] Author and Article Information
Yi Lu

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

J. Mech. Des 128(3), 574-580 (Jul 24, 2005) (7 pages) doi:10.1115/1.2181993 History: Received February 17, 2005; Revised July 24, 2005

## Abstract

A novel 3-SPU/3-SPU parallel manipulator with 3-DOF is presented. The CAD variation geometric approach and analytic approach are used for solving its workspace, position, velocity, and acceleration. First, a simulation mechanism of the 3-SPU/3-SPU parallel manipulator is created by using CAD variation geometric techniques, and its kinematic characteristics are analyzed. Second, the workspace of the 3-SPU/3-SPU simulation mechanism is solved and its singularity is analyzed. Based on the kinematic characteristics of the 3-SPU/3-SPU simulation mechanism, some analytic formulas are derived for inverse and forward solving position. Third, Jacobian matrix and Hessian matrix are derived for solving velocity and acceleration. Finally, a calculation example is given. These simulation and analytic results prove that the novel 3-SPU/3-SPU parallel manipulator has a relatively large workspace and relatively large capacity of loadbearing, and are relatively easy to control. The result of computer simulation solving position is the same as that of the analytic solution. The simulation mechanism can be used to solve workspace, analyze characteristics of a moving platform, and derive a kinematic formula. The CAD variation geometric approach is straightforward, and is advantageous from the viewpoint of accuracy and repeatability without compiling any computer program.

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## Figures

Figure 5

The kinematic parameters vs time of m of the 3-SPU/3-SPU parallel manipulator. (a) Extension of driving limbs. (b) Position of m. (c) Velocity of m. (d) acceleration of m.

Figure 1

The 6-SPU parallel manipulator

Figure 2

The 3-SPU/3-SPU parallel manipulator

Figure 3

The simulation mechanism of parallel manipulator (a) and its one third of upper and lower workspace boundary surface (b)

Figure 4

The 3 upper and 3 lower surfaces of workspace for the 3-SPU/3-SPU parallel manipulator (a) and its top view (b)

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