Abstract

This paper presents a simple and effective closed-form method for solving direct kinematics of parallel mechanism (PM) based on ordered single-open-chain units (SOCs). The method includes two steps. The first step is to establish the kinematic constraint equations that contain the least virtual variables of a PM, by using the modelling principle based on ordered SOCs. The second step is to derive and solve a nonlinear equation with one unknown from the constraint position equations by means of the software Mathematica. The method is applicable for direct kinematics of various complex planar and spatial PMs.

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