Kinematics of 3-PRS parallel manipulators with integrated parasitic motions via screw theory

Abstract

Kinematic behavior of a 3-PRS parallel manipulator is investigated with particular emphasis on the characterization and analysis of the so-called parasitic motions. These unintended displacements, arising from the mechanism’s inherent geometric and structural constraints, play a critical role in determining the overall accuracy and performance of parallel manipulators. The displacement analysis is performed using two distinct strategies based on simple closure equations, enabling the derivation of expressions for the parasitic displacements of the moving platform. Subsequently, the input-output velocity relationship is obtained by applying the theory of screws. This expression is independent of passive joint rates and can be directly applied to both inverse and forward velocity analyses. Numerical examples, validated using specialized software such as ADAMS,^tmare presented to demonstrate that the socalled parasitic motions are both predictable and computable, rather than the result of unexpected or random behavior in the zero-torsion mechanism.