Examining the Planar Kinematic based on dual Quaternions

Kinematics studies the motion of a rigid object, such as displacement, velocity, acceleration, etc. A general planar motion can be defined as a combination of translation and rotation. Planar motion is widely used in many fields. Since most mobile robots move on flat terrain, many grippers and kinematic linkages use planar motion. The dual quaternion is the generalization of the quaternion and is used in various fields. In this paper, we introduce a new approach to planar motions by using the dual quaternion to study the pole points and pole trajectories, the triple coordinate system and the canonical system, and find the Euler-Savary equation.