A mechanical manipulator can modeled as an open-loop articulated chain with several rigid bodies (links) connected in series by either revolute or prismatic joints driven by actuators.One end of the chain is attached to a supporting base while teh other end attached with a tool (end -effector) to manipulate objects or perform assembly tasks.The relative motion of the joints results in the motion of the links that positions the hand in desired orientation.In most ofthe robotics applications ,one is interested inthe spatial description of the end-effector of the manipulator with respect to a fixed co-ordinate system.

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 regards to the forces/moments that cause 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-variable space and the position and orientation of the robot arm. This chapter addresses two fundamental questions of both theoretical and practical interests in robot arm mechanism.