Kinematic and Static Analysis of a Cable-Driven 2-X Tensegrity Manipulator for Two Actuation Strategies

Abstract

This paper analyzes the instantaneous kinematic and static performance of a two degree-of-freedom serial manipulator composed of anti-parallelogram (or X-) tensegrity joints and remotely driven with cables. Two actuation schemes with 4 cables and 3 cables, respectively, are considered for this manipulator. The physical limitations on the velocities and forces of the actuating cables are mapped onto the task space of the manipulator, to quantify the corresponding velocity and force-application capabilities of the end-effector. A comparative study is carried out between the 4-cable and 3-cable actuation schemes in terms of their velocity and force performance.

Design Considerations and Workspace Computation of 2-X and 2-R Planar Cable-Driven Tensegrity-Inspired Manipulators

“…negative) in Eq. (33). Thus, the condition of equilibrium (α 1 , α 2 ) can be satisfied only when G i ∈ Γ i , Γ i for i = 1, 2.…”

“…The limiting condition(s) of stability can be found from the vanishing of the determinants of these matrices as explained in [32], [33]. Their zero-level sets can be plotted in the joint space to distinguish between the stable and unstable configurations for the manipulator.…”

“…When all the parameters (bar dimensions, springs, cable forces) of the 2-X manipulator are defined, its SWFW can be obtained by using the method described in [32], [33]. The important steps involved are summarized in the following:…”

“…In the literature, it is a common strategy to inscribe a regular shape, such as a disk, inside the workspace and use its dimensions for quantification [35]. Since the SWFW is in the form of polygons [32], an open-source c++ library polylabel has been used to find the maximally inscribed disk(s) inside it 4 . The inscribed disks shown in Fig.…”

“…Similar to the X-joint, the set of all feasible springs for the R-joint is obtained from χ a ∪ χ b . 31) and (32). Unlike in the case of 2-X manipulator, these coefficients involve only two varying angles (α 1 , α 2 ) and three constant angles (β 0 , β 1 , β 2 ) in the offsets and joints (shown in Fig.…”