This paper presents a novel approach to remodel the manipulator kinematics and solve the feasible motions of the manipulator at singular configurations. This method based on degenerate direction motion elimination to handle series manipulator singularity problem. By using this method, the unachievable components of the commanded motion are removed, while an exacted inverse kinematic solution is used for the achievable motion components at singular configurations. The main idea is to analyze joint axis linear dependence by using classified line varieties so as to recognize these singularity directions, and identify the task space feasible motions by using reciprocal screws and motion constraint equations, then, we eliminate the corresponding columns and rows of the singular Jacobian matrix so that the mapping between task space feasible motions and the joint space motions becomes uniquely defined. If one or more linear axis vectors may be described linear dependent by other remaining axis vectors, those will result in singular configurations of the manipulator. Hence, the corresponding columns of Jacobian matrix will be deleted, and also the rows corresponding to the degrees of freedom that the manipulator lost near singular configuration are dropped. Thus, if the manipulator loses one of six-degree of freedom (i.e. there is one singular point), we drop that constraint from the Jacobian yielding a five-by-five full rank matrix. In the end, some simulation results for PUMA. manipulator are given to demonstrate the effectiveness of this method.
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