摘要：Recently, there has been considerable effort to bring together quaternion-based representations of spatial displacements with curve design techniques in computer Aided geometric Design (cAGD) to develop methods for synthesizing freeform cartesian motions. These methods have a wide range of applications from computer graphics,cartesian motion planning for robot manipulators to task specification and motion approximation for spatial mechanism design. This paper compares the use of quaternions, dual quaternions, and double quaternions for freeform motion synthesis in a cAD environment.