Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures

[+] Author and Article Information
V. Parenti-Castelli, C. Innocenti

Università di Bologna, Viale Risorgimento, 2, 40136, Bologna, Italy

J. Mech. Des 114(1), 68-73 (Mar 01, 1992) (6 pages) doi:10.1115/1.2916927 History: Received March 01, 1990; Online June 02, 2008


The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

Copyright © 1992 by The American Society of Mechanical Engineers
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