Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work

Abstract

Inverse dynamics of a general model of a spherical star-triangle (SST) parallel manipulator (Enferadi and Akbarzadeh Tootoonchi, Robotica 27:663-676, 2009) is the subject of this paper. This manipulator is of type 3-RRP, has good accuracy and relatively a large workspace which is free of singularities (Enferadi and Akbarzadeh Tootoonchi, Robotica, Revised paper, 2009). First, inverse kinematics utilizing the angle axis representation is solved. Next, velocity and acceleration analysis as well as link Jacobian matrices are obtained in invariant form. Finally, a systematic approach based on the principle of virtual work and the concept of link Jacobian matrices is presented. This method allows elimination of constraint forces and moments at the passive joints from motion equations. It is shown that the dynamics of the manipulator can be reduced to solving a system of three linear equations with three unknowns. Moreover, a computational algorithm for solving the inverse dynamics is developed. Two examples with different trajectories for the moving spherical platform are presented and motor torques are obtained. Results are verified using a commercial dynamics modeling package.

Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement

“…Therefore, we need to formulate the dynamics equations in terms of the generalized coordinates of joints and their time derivatives. Unlike other common dynamics methods such as principle of virtual work [10], solution of the direct dynamics problem does not require directly solving the direct kinematics problem. Additionally, the dynamics equations are formulated in terms of only the actuated joints [11].…”

“…In the first example, a robot trajectory is given and inverse dynamics using the NOC is solved to obtain required motor torques. Results are next verified with inverse dynamics using the virtual work method [10]. In the second example, motor torques, obtained from the inverse dynamics of the first example, are used as input for the direct dynamics solution using the NOC.…”

Closed-form dynamic formulation of spherical parallel manipulators by Gibbs-Appell method

“…Lagrangian based procedures need symbolic matrix differentiating to obtain the coriolis matrix of dynamic model, which is very difficult to obtain, [14]. Virtual work is the most frequently used method for dynamic modeling of spherical parallel robots, [15], [16]. In [15] the dynamic formulation leads to a recursive model, which is not in closed form, and therefore, not computationally efficient.…”

Dynamic modeling and computational efficiency analysis for a spatial 6-DOF parallel motion system

“…To derive the dynamic model of parallel manipulator, various methods for modeling of multi-rigid body systems, such as Lagrange equation, principle of virtual work, Newton-Euler, and Kane approach, are presented [7][8][9][10]. Dasgupta and Mruthyunjaya [11] derived a closed-form dynamic equation of parallel manipulator by using Newton-Euler method.…”