Singularity analysis of 6-SPS mechanism with 2 S-pairs clearance

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (7) : 130-137.

Zhao De-sheng Wu Rong-jun

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Abstract

The pose matrix of 6-SPS mechanism is described by quaternion method, where the matrix and vector coordinates are expanded to the 4-dimensional form to derive the motion equations of mechanism without clearance. Then, the novel kinematic Jacobi matrixes JA and JB of the mechanism are achieved. On this basis, the movement coefficient matrixes of two S-pairs co-linkage and different-linkage mechanism are derived through continuous contact model. Each determinant of movement coefficients is expanded respectively. Subsequently, the trajectory equations containing the first category of singular and the second category of singular of clearance mechanism are derived separately. Using MATLAB software, the three-dimensional track surface of the first category of and the second category of pose-attitude singular trajectories at a given location of the mechanism is obtained. The comparison between two types of singularity trajectory surfaces containing the clearance mechanism highlights that the influence of mechanism clearance on the second category of singular is greater than the first category. Among the two types of singularity tracks, the influence of mechanism clearance in different-linkage S pairs is greater than that in co-linkage S pairs. The singular points on the trajectory surface of mechanism without clearance are considered as reference points. Comparing the singular points with each other on the singularity trajectory surface containing clearance mechanism corresponding to the reference points, a singular area about the reference point can be found.

Key words

quaternion ;singularity / parallel mechanism with clearance / Jacobi matrix / singular area

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Zhao De-sheng Wu Rong-jun . Singularity analysis of 6-SPS mechanism with 2 S-pairs clearance[J]. Journal of Vibration and Shock, 2016, 35(7): 130-137

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