Chapter 6 : Dynamic Simulation Environment

Previous kinematic and dynamic analysis has demonstrated the singularity-free workspace and the high force-bearing characteristics of the Wrist. This chapter completes the dynamic model of the Carpal Wrist by presenting a closed-form solution and algorithm to the time response (forward dynamic) problem. With this model, simulation of the Wrist in an application environment can be performed to generate various control-system algorithms. An example of such an application would be to create a neural network control device trained via the forward dynamic model. This forward dynamic model will be developed from the equations of motion which have been derived in closed form by direct application of Lagrange’s equations to the kinematic model. The dynamic model assumes a relatively massive tool and considers all gravitational, inertial, Coriolis and gyroscopic effects. The forward dynamics presents the equations of motion in a form that is evaluated over time to determine trajectory information based on actuator inputs. The results of these equations is a simulation environment that can represent the Wrist in application for modeling, design, and control purposes.