Impact dynamics of flexible-joint robots

In this paper the dynamic analysis of a flexible-joint robot colliding with its environments is presented. The system considered here is an n-rigidlink manipulator driven by n DC-motors through n revolute flexible-joints. The flexibility of each flexible joint is modelled as a linearly elastic torsional spring. 2n generalized coordinates are introduced to identify the configuration of the robot. The concept of impulse potential energy is introduced, and the generalized impulse-momentum equations along with the equation involving coefficient of restitution are used to establish the complete mathematic model for dealing with the case of a flexible-joint manipulator colliding with its environments (such as the ground, another manipulator, and so on). Solving for this mathematic model, one can obtain the jump discontinuities in system generalized velocities and the impulses at the impact points explicitly. To validate the algorithm presented in this paper, the dynamic simulation of a robot involving impact with its environments is given as an example.