Kinematics Analysis and Optimization of a 3-DOF Planar Tensegrity Manipulator under Workspace Constraint

Tensegrity mechanisms (TM) are well-appraised for their compliance and lightweight, making their design theory a hot research topic recently. However, due to unconstrained DOFs, the design and analysis of TMs are generally more complicated than traditional mechanisms composed of rigid links and joints. A compact 3-DOF tensegrity manipulator is introduced and an advanced two-step kinematic modeling method is proposed in this paper. This method is first assumed that bars and cables are rigid to estimate the equilibrium state using the energy-based method. Then, the flexibility of bars and cables is considered, and the force density method equations are solved utilizing the equilibrium state obtained by the previous step as the initial guess of iteration for fast computation. Based on the two-step method, the performances of the TM, such as workspace, manipulability, potential energy, and stiffness, are analyzed. Thereafter, the installation position and size of the manipulator are optimized under the workspace constraint. In the optimization process, discrete points on the prescribed task workspace contour are used to simplify the constraint to improve computational efficiency. Finally, study cases are investigated to validate the proposed method, and the feasibility of the discrete sampling method for constraint simplification is also verified.