Kinematic Parameter Identification for Parallel Robots With Passive Limbs

Abstract

Parallel robots have passive joints and even passive limbs. Current calibration methods seldom consider the resulted identification and compensation properties and thus accuracy improvement is affected. This letter adopts finite and instantaneous screw (FIS) theory as mathematical tool. A generalized error model is built based on the reciprocal property between twist and wrench. Parameter identifiability is proved by discussing linear dependency of identification mapping matrix among limbs and within limb. Maximum independent geometric errors number of any parallel robot is 4 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> +4 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> +2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> +6, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> are the numbers of revolute, helical and prismatic joints. It is found that joint twist errors of passive limbs are not compensable for the indirect compensation. Simulations and experiment show that the presented FIS-based calibration method with identifiable and compensable parameters significantly improves accuracy of the parallel robot. In addition, errors of passive limbs have no contribution to the accuracy improvement and can be ignored from the modeling phase.