Optimization of the Workspace Volume of 3r Manipulators Using a Hybrid Methodology

A fundamental feature of a manipulator is the capacity of its workspace because it influences on the manipulator design, in the manipulator position in the work environment and in the its dexterity. In the case of 3R manipulators, it is represented by a revolution solid. Thus, in this paper the workspace volume is calculated based on the area of its radial section. An optimization problem is formulated with the objective of determining the geometric parameters of 3R manipulators so that the maximum workspace volume is obtained. The maximization is accomplished forcing the workspace to occupy the largest set of points inside of a pre-established region, which in this case is a cylinder whose axis coincides with the axis of rotation of the workspace. In the optimization procedure a function that establishes the difference between the volume of the pre-established region and the volume of the workspace is minimized. An optimization strategy that considers a hybrid methodology employing two techniques: sequential quadratic programming (SQP) and differential evolution (DE) is proposed. Additional constraints are included to obtain manipulator dimensions within practical values, and to specify limits at the workspace. Application examples are presented to validate the proposal methodology.