Analytical Mobility Analysis of Bennett Linkage Using Geometric Algebra

摘要

It has been challenging to obtain an analytical or closed-form expression of the motion space of a Bennet linkage because it is over-constrained and has complex geometric conditions. This paper presents an analytical mobility analysis of the Bennet linkage using geometric algebra. Frist, the Bennet linkage is regarded as a 2-RR (R: revolute joint) parallel mechanism and the limb motion space is the join of two twists associated with the two revolute pairs. Then, the motion space of the output link of the Bennet linkage is obtained by using meet operator to calculate the intersection of the two limb motion space. Compared to the constrained screw-based method, the use of a meet operator results in fewer steps, thus simplifying the computation. This intersection presents an analytical or symbolic expression of the motion space of the Bennet linkage with straightforward geometric interpretations.