Kinematic design of assembly machine from task specifications using Lie algebra

This paper presents a new method for kinematic synthesis of mechanisms from assembly task specifications in a conceptual design. The assembly task is classified into continuous path or positioning task. The former is the task that moves a mechanical part along a required path, and the latter is the task that puts the part in a particular position or orientation. The authors formulate them mathematically using Lie algebra and propose a method for generating an initial solution of the mechanism that can perform the specified tasks. By applying this solution to the analysis and synthesis procedure proposed in our previous report, a number of equivalent mechanisms can be derived. Finally, in order to evaluate the usefulness of the proposed method, it is applied to an example of kinematic design of an assembly machine.