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¡¡¡¡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£º 1. Forward analysis£º 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£º 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£¿