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

Abstract

Spherical Parallel Robot (SPR) is a complex but widely used type of manipulators that performs only rotational motion. Dynamic analysis of SPR has a vital role in mechanical design, model-based controller, identification and fault detection of such robots. Complexity of SPR kinematic structure makes traditional dynamic modeling methods such as Newton-Euler, virtual work and Lagrange formulations a prohibitive task. In this paper a new procedure for deriving closed form dynamics of general SPR using Gibbs-Appell method is presented. The proposed method does not require any recursive computation or symbolic manipulation and dynamic matrices of the robot is directly derived in an explicit form. By using the proposed method, closed form dynamic formulation of a general 3DOF SPR, known as agile wrist, is obtained and it is verified for an arbitrary trajectory. The unique feature of the method presented in this paper, makes it promising to be used for other parallel manipulators.

A Position-Control Based Approach to Haptic Rendering of Stiff Objects

“…In addition, the dynamics of a parallel mechanism (PM) is mostly estimated by iterative or recursive methods, which introduce error and slow down the computation further when it is hard to converge. For well-known PMs like the Stewart-Gough platform [19] or Agile-Wrist [20], a closed-form (or explicit/analytical) solution of the dynamic model can be derived, thus the evaluation is faster than using numerical methods. However, such solution relies on the symmetry of the actual mechanism and cannot be generalized to work on more general PMs.…”

Kinematic and workspace analysis of DIAMOND: An innovative eye surgery robot

“…7; As it is seen in this figure, this measure get close to zero only at the down end of the curves. Such configurations may be determined by using equation (15). Upon determining such configurations the result indicate that such singularity happens at the maximum value of γ.…”

“…To represent some features of the robot, motion analysis of the spherical structure of the robot has been investigated. The analysis of spherical mechanisms have been investigated by others [15], [16], [6], [17].The kinematic analysis of DIAMOND is investigated by spherical trigonometry which make the analysis much simpler rather than cartesian based methods.…”

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“…Pedrammehr et al [22] developed the closed-form dynamics of hexarot manipulators by adopting Alembert's form of virtual work principle and performed the validation in SimMechanics. Except for the above methodologies, Kane method [23,24], screw theory [25], Gibbs-Appell [26,27], and Hamilton method [28] have also been commonly adopted in dynamic analysis.…”