A novel spherical parallel manipulator: forward position problem, singularity analysis, and isotropy design

Enferadi, Javad; Akbarzadeh, Alireza

doi:10.1017/s0263574708005031

Cited by 27 publications

(23 citation statements)

References 17 publications

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“…For simplicity and ease of illustration, we choose the isotropic design of the SST manipulator [1]. Based on the algorithm outlined in the previous section, a computer program is developed using MATLAB software.…”

Section: Numerical Examplesmentioning

confidence: 99%

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

Enferadi

Akbarzadeh

2010

Nonlinear Dyn

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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.

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Section: Numerical Examplesmentioning

confidence: 99%

“…For example, in the case of satellite antenna tracking, the orienting system must be accurate and be able to carry a rather large payload. This has motivated us to design the SST manipulator that offers certain advantages [1,2]. To control and further improve the SST manipulator, dynamics of the manipulator must be determined.…”

Section: Introductionmentioning

confidence: 99%

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

Enferadi

Akbarzadeh

2010

Nonlinear Dyn

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“…The Jacobian matrices J 1 and J 2 are obtained by velocity analysis and reported in ref. 1 as follows:…”

Section: Jacobian Matricesmentioning

confidence: 99%

“…The forward kinematics problem, isotropic design, and singularity analysis of this manipulator has been previously investigated and reported in ref. [1]. We select the isotropic design because it is the superior design and obtain its performance indices.…”

Section: Introductionmentioning

confidence: 99%

Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator

Enferadi

Akbarzadeh

2010

Robotica

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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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“…Due to the closed-loop structure and kinematic constraints of PKMs, the derivation of dynamic equations is quite complicated. There are three main methods of formulation of the dynamical equations; namely, Newton-Euler laws, the Lagrangian formulation, the principle of virtual work [18][19][20][21][22][23][24][25] and Kane's method [26]. The Lagrangian formulation allows eliminating all of the reaction forces and moments at the beginning.…”

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confidence: 99%