![]() In this paper, we derive sufficient conditions for the optimal solution of the kinematic control of a redundant manipulator. ![]() One of the problems is a switching problem, i.e., an undesirable configuration change from a maximum value of a performance measure to a minimum value may occur and cause an inverse kinematic solution to be unstable. SummaryThe algorithms of inverse kinematics based on optimality constraints have some problems because those are based only on necessary conditions for optimality. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms. The new method has the following features: (1) using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency and (2) compared with the algebraic method, it has evidently reduced the difficulty of deducing formulas. ![]() All the real solutions to inverse kinematics problems of the general 6R serial robot or forward kinematics problems of the general 7R single-loop mechanism can be obtained. Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on a one-dimension searching algorithm. The inverse kinematic analysis of the general 6R serial robot has been a very significant and important problem in the theory of the spatial mechanisms.
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