Effective Tool-Point Acceleration of Serial Chain Mechanisms Based on Basic Geometric Transformations

In this paper, a method to manage the actuator parameters of a serial chain mechanism composed of revolute joints to achieve improved responsiveness characteristics (acceleration capability) based on the basic geometric parameters of the mechanism is presented. Here, an analytic framework presented by the authors in an earlier work, which exploits the geometric structure of this type of mechanism is extended to address the tool-point mass and acceleration. The manipulator’s geometry is reduced to a set of lengths, which are representative of the mechanical gains associated with the manipulator and they, along with the transmission ratio of the actuators, are used to map the actuator parameters to their effective values at the tool-point where a direct comparison to the task requirements can be made. With this method, minimal computations are required to evaluate the system’s performance since only the forward kinematic computations are required. The effects of the actuator transmission ratio parameter on the effective tool-point force, mass, and acceleration are investigated for a six-DOF serial chain manipulator. Through this case study, it is demonstrated how the transmission ratio is managed to balance the system’s effective tool-point force and mass to obtain an optimal tool-point acceleration. In addition to the investigation of the effects of the actuator parameters, the method is shown to be useful in the solution of the configuration management or modular design problem since the exponential design space can be searched for a globally optimal solution with minimal computations. The goal of the configuration management problem is to quickly configure and/or reconfigure a robotic manipulator from a finite set of actuator modules.