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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.
Kinematic models are essential for controlling the movements of robots. Robotics engineers use forward kinematics to calculate the positions and orientations of a robot's end-effector, given specific joint angles, and inverse kinematics to determine the joint movements necessary for a desired end-effector position. These calculations allow for ...
The kinematics equations for the series chain of a robot are obtained using a rigid transformation [Z] to characterize the relative movement allowed at each joint and separate rigid transformation [X] to define the dimensions of each link. The result is a sequence of rigid transformations alternating joint and link transformations from the base ...
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The kinematics equations for a parallel chain, or parallel robot, formed by an end-effector supported by multiple serial chains are obtained from the kinematics equations of each of the supporting serial chains. Suppose that m serial chains support the end-effector, then the transformation from the base to the end-effector is defined by m ...
The JPL mobile robot ATHLETE is a platform with six serial chain legs ending in wheels. The arms, fingers, and head of the JSC Robonaut are modeled as kinematic chains. The movement of the Boulton & Watt steam engine is studied as a system of rigid bodies connected by joints forming a kinematic chain.
Victor Scheinman's MIT Arm, built for MIT's Artificial Intelligence Lab ca. 1972, the first arm designed with a 321 kinematic structure. 321 kinematic structure is a design method for robotic arms (serial manipulators), invented by Donald L. Pieper and used in most commercially produced robotic arms.
The Stanford arm is an industrial robot with six degrees of freedom, designed at Stanford University by Victor Scheinman in 1969. [1] The Stanford arm is a serial manipulator whose kinematic chain consists of two revolute joints at the base, a prismatic joint , and a spherical joint .