For a robotic system, the complete description of the end-effector motion requires six independent parameters, while the desired end-effector motion for a task often needs less than 6 d.o.f. Therefore, the end-effector motion can be divided into desired motion and undesired motion. The end-effector motion is transformed from the joint motions. In this paper, the efficiency of the joint motions to implement the desired motion is investigated and a new concept called motion purity is proposed to measure this efficiency. The new concept is more comprehensive and direct than other existing performance measures, such as the volume of workspace and manipulability. It is appropriate as a design objective at various phases in designing a robotic mechanism. The tripod machine tool is studied and its structure is optimized from the viewpoint of the motion purity.

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