Optimal Design of Three-Link Planar Manipulators Using Grashof’s Criterion

Abstract

The design of robotic manipulators is dictated by a set of pre-determined task descriptions and performance parameters. These performance parameters are often defined in terms of workspace dexterity, manipulability, and accuracy. Many serial manipulator applications require that the manipulator have full dexterity about a work piece or a pre-defined trajectory, that is, to approach the given point within the workspace with all possible orientations about that point. Grashof’s criterion defines the mobility of four-link closed chain mechanisms in relation to its link lengths. A simple assumption can convert a three-link serial manipulator into a four-link closed chain so that its mobility can be studied using Grashof’s criterion. With the help of Grashof’s criterion, it is possible not only to predict and simulate the mobility of a manipulator during its design, but also to map and identify the fully-dexterous regions within its workspace. Mapping of the dexterous workspace is helpful in efficient task placement and path planning. Next, the authors propose a simple algorithm using Grashof’s criterion for determining the optimal link lengths of a three-link manipulator, in order to achieve full dexterity at the desired regions of the workspace. Finally, the authors test the generated design by applying joint angle limitations.