On n-link planar revolute robot: Motion equations and new properties

Multilink planar revolute robots or multilink pendulum-type robots are interesting benchmark systems for control and robotics. In this paper, we present an elementary derivation for motion equations of an n-link planar robot with all rotational joints moving in the vertical plane. Moreover, we prove several known properties and present several new properties on the mechanical parameters in the motion equations of the robot. These results are believed to be useful to study the problems of an n-link planar robot with one or more underactuated joints such as the controllability and the swing-up and stabilizing control regarding the changes of the number and location of actuators of the robot.