Kinematics analysis Robot arm kinematics deals with the analytical study of the geometry of motion of a robot arm with respect to a fixed reference coordinate system as a function of time without regard to the forces/moments that causes the motion. Thus， it deals with the analytical description of the spatial displacement of the robot as a function of time， in particular the relations between the joint space and the position and orientation of the end-effector of a robot arm. In kinematics， we consider two issues： 1. Forward analysis： for a given manipulator， given the joint angle vector q（t）=（q1（t）， q2（t）， …。， qN（t））T and the geometric link parameters， where n is the number of degrees of freedom， what is the position and orientation of the end-effector with respect to a reference coordinate system？ 2. Inverse analysis： given a desired position and orientation of the end effector and the geometric link parameters with respect to a reference coordinate system， can the manipulator reach the desired manipulator hand position and orientation. And if it can， how many different manipulator configurations will satisfy the same condition？