Udwadia Kalaba Approach for Parallel Manipulator Dynamics

Abstract

A novel UdwadiaKalaba approach for parallel manipulator dynamics analysis is presented. The approach segments a parallel manipulator system into several legsubsystems and the platform subsystem, which are connected by kinematic constraints. The UdwadiaKalaba equation is then used to calculate the constraint forces due to the constraints. Based on this, the equation of motion, which is an explicit (i.e., closed) form, can be formulated. The method allows a systematic procedure to generate the dynamic model for both direct dynamics and inverse dynamics without invoking additional variables (such as multipliers or quasivariables), nor does it require projection. A classical parallel StewartGough platform is chosen to demonstrate the feasibility and advantages of this approach.