Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs

Abstract

A novel method is proposed for real-time solution of direct kinematics problem of Stewart platform (SP) using six measurements on three legs’ joints consisting of the rotations of three legs in two directions. After the application of the method on a laboratory sample SP, it is observed that the method is preferable to the conventional method that uses the length measurements of all six legs, in the grounds of industrial applicability. It is due to simpler implementation, less expense, easier maintenance, and stress-free assembly. The algorithms of both forward and inverse kinematics are fully derived based on geometric relationships between the platform states and the measurement data. The sensitivity to the measurement errors is analyzed theoretically and is applied through a computer simulation to several configurations of the sample SP which are uniformly distributed in the workspace. The variances of measurement errors for those configurations are compared between the conventional and proposed methods and it is observed that: the proposed method operates more accurate in position measurement especially in lateral movements. Additionally, the proposed method is not too sensitive to direction of movement and geometry of the SP.