Selecting active members to drive the mechanism displacement of tensegrities

Abstract

Based on the quasi-static assumption, the mechanism motion of tensegrities driven by the length actuation of internal active members is discussed in this paper. The self-stress and mechanism characteristics of a tensegrity are guaranteed by maintaining the zero eigenvalues of the state matrix of each configuration on a kinematic path. The sensitivity matrix between the eigenvalues of the state matrix and the joint displacements is given, and it is shown that the displacement causes only second- and higher-order changes to the zero eigenvalues. A strategy is proposed to trace the shortest path of mechanism displacement towards the target configuration of the tensegrity. The moving direction of mechanism displacement that is closest to the direction from the current configuration to the target configuration and the deviation of this direction can be calculated based on arbitrary bases of the null and row spaces of the compatibility matrix. A method for quickly constructing the basis of the row space of the compatibility matrix consisting of passive members is put forward to rapidly calculate the deviation between the current direction of mechanism displacement and the direction towards the target configuration after an active member is converted into a passive one. When the number of active members is limited, a one-by-one exclusion method is proposed to select active members to minimize the direction deviation of mechanism displacement. A four-stage quadriprism tensegrity tower and an icosahedron tensegrity are employed as illustrative examples. The proposed method is used to select active members and trace the paths of mechanism displacements, and its validity is verified by the results.