robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. j. m. mccarthy, 1990, introduction to theoretical kinematics, mit press, cambridge, ma. the emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques. the relationship between mass and inertia properties, motion, and the associated forces and torques is studied as part of robot dynamics. ==kinematic equations==  a fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. these non-linear equations are used to map the joint parameters to the configuration of the robot system. kinematics equations are also used in biomechanics of the skeleton and computer animation of articulated characters. forward kinematics uses the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters.john j. craig, 2004, introduction to robotics: mechanics and control (3rd edition), prentice-hall. the reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics. the dimensions of the robot and its kinematics equations define the volume of space reachable by the robot, known as its workspace. there are two broad classes of robots and associated kinematics equations serial manipulators and parallel manipulators. other types of systems with specialized kinematics equations are air, land, and submersible mobile robots, hyper-redundant, or snake, robots and humanoid robots. ===forward kinematics===  forward kinematics specifies the joint parameters and computes the configuration of the chain. for serial manipulators this is achieved by direct substitution of the joint parameters into the forward kinematics equations for the serial chain. for parallel manipulators substitution of the joint parameters into the kinematics equations requires solution of the a set of polynomial constraints to determine 
Robot_kinematics