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.
In this paper, a novel spherical parallel manipulator and its isotropic design is introduced. This manipulator has good accuracy and relatively a larger workspace which is free of singularities. Utilizing spherical configuration the forward position problem is solved by equivalent angleaxis representation and Bezout's method which leads to a polynomial of degree 8. Two examples are given, one for isotropic and one for nonisotrpoic design. The first case results in eight real solutions, therefore, the polynomial being minimal. Using invariant form, we study acceleration analysis, conditions for singularity and find infinite isotropic structures. Accuracy and workspace analysis are also performed and are shown to have good global conditioning index and relatively large workspace. Using isotropic design and singularity requirements, we show the workspace of isotropic design is free of singularity.
In this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663-676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global conditioning index (GCI) of the manipulator is calculated and compared with another SPM. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. A continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano's theorem. The mathematical model is verified by finite element model. Finally, using mathematical model, kinematics stiffness index (KSI), and global stiffness index (GSI) are evaluated.
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