Kinetics of planar constrained robotic mechanisms with multiple closed loops: An experimental study

Abstract

This paper presents a direct and straightforward approach for deriving the kinetic equations of the planar mechanisms comprising multiple kinematic closed loops. What distinguishes this research from similar works is that it explores the mechanisms with several constrained joints in their structure. In this respect, after disassembling the said mechanisms into a specific number of closed chains, the constrained joints of each chain are analyzed kinematically and dynamically. Considering the governing constraints of each loop in the system, the recursive Gibbs-Appell methodology is employed to extract the equations of motion for that loop. The most important feature of the recursive formulation developed in this paper is its ability to symbolically derive each chain's motion equations irrespective of the number of links present in that chain. In the next step, with the consideration of the dynamic coupling between the chains, the motion equations of the separate chains are combined in order to derive the main mechanism's kinetic equations. Finally, by constructing a sample mechanism, the theoretical results are compared with the test results obtained by this experimental setup.