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An algebra is defined for use in problems of manipulator kinematics. With this algebra, one can program the solution to the kinematics in position problems, and use this same program to solve the kinematics problems in velocity and acceleration. The inverse kinematics part of the program can be used to obtain any order time-derivative of the joint positions. Some of the properties of the algebra are shown and functions of the elements of the algebra are defined. The solution to the forward and inverse kinematics problem is presented, and the use of the Ada programming language is discussed.>
Michael Walker (1988) studied this question.