Forward kinematic analysis of a 3-RRRS mechanism with subordinate driving variables using a computer-aided geometric method

摘要

The 3-RRRS mechanism (RRRS refers to kinematic pairs of a branched chain consisting of three R pairs (Rotational pairs) and one S pair (Spherical pair), successively) is used between a moving platform and a static platform, through which six-dimensional motion of the moving platform relative to the static platform can be achieved. Selecting six independently drivable joints from nine active joints makes it problematic to deal analytically with the kinematics of the 3-RRRS mechanism. In this article, a novel computer-aided geometric method for kinematic analysis is developed. This method can automatically detect the independently drivable joints for arbitrary kinematic chains. This method can be easily implemented compared to the analytical method of the forward kinematics. Based on the constraint relationship of the 3-RRRS mechanism, a general 3-RRRS mechanism digital model is built in the SolidWorks Application Program Interface embedded Visual Basic environment, in which the platform sizes and active driving angles are driven by the parameterized model, to make the moving platform move to the corresponding pose. After the pose of the moving platform is confirmed, the coordinate system is built in a preliminary sketch. The parameters are measured by the SolidWorks measuring functions, and the pose of the moving platform is obtained by combining homogeneous matrices. Using the computer-aided geometric method, the detailed kinematics formula is not required. The accuracy and efficiency of the computer-aided geometric method were assessed with some examples of kinematic analysis for the 3-RRRS mechanism. The results showed that the proposed method obtained competitive precision and calculation time to the analytical method and is beneficial as a convenient solving process. By using Visual Basic programming, a reachable poses analysis of the mechanism can be merged into the kinematics analysis system of the computer-aided geometric method. The computer-aided geometric method could be widely applied to kinematics analysis of mechanisms.