A Closed-Form Solution for the Direct Kinematics of a Special Class of Spherical Three-Degree-of-Freedom Parallel Manipulators

Gosselin, Cle ́ment M.; Gagné, Martin

doi:10.1007/978-94-011-0333-6_24

Cited by 28 publications

(25 citation statements)

References 6 publications

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“…From equation (16) the inverse kinematics solutions are calculated using equation (10) in terms of actuated joint angles θ i in degrees as follows: [17] Analysing above calculated roots of equation (16), it can be observed that positive roots, i.e. positive actuated joint angles θ i , are equal to the initially given input angles θ 1 = 95 deg., θ 2 = 110 deg.…”

Section: B Inverse Kinematic Solution Of the Agile Wristmentioning

confidence: 99%

An approach for obtaining unique kinematic solutions of a spherical parallel manipulator

Niyetkaliyev

Shintemirov

2014

2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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In this paper an approach for obtaining unique solutions to forward and inverse kinematics of a spherical parallel manipulator (SPM) system with revolute joints is proposed. Kinematic analysis of a general SPM with revolute joints is revisited and the proposed approach is formulated in the form of easy-to-follow algorithms that are described in detail. A graphical verification method using SPM computer-aideddesign (CAD) models is presented together with numerical and experimental examples that confirm the correctness of the proposed approach. It is expected that this approach can be applied to SPMs with different geometries and can be useful in designing real-time control systems of SPMs.

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Section: B Inverse Kinematic Solution Of the Agile Wristmentioning

confidence: 99%

An approach for obtaining unique kinematic solutions of a spherical parallel manipulator

Niyetkaliyev

Shintemirov

2014

2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics

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“…Subsequently, the coordinates of points B i , C i , D i , E i , and F i , i = 1, 2, 3, are calculated according to (19) 2, 3, are defined in the MATLAB environment using the Multi-Parametric Toolbox [50], which implements computational geometry functions. This toolbox is also used to easily implement the QP that calculates the Euclidean distance between any two segments by setting δ = 14 mm, chosen based on the Agile Wrist SPM prototype geometry given in Section IV-B.…”

Section: Workpace Computationmentioning

confidence: 99%

“…the Agile Wrist/Eye, the complexity of forward and inverse kinematic problems reduces significantly and closed-form analytical solutions can be obtained [19]. An approach for producing a unique solution to the forward kinematics of the Agile Eye SPM is reported in [25].…”

Section: Introductionmentioning

confidence: 99%

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Shintemirov

Niyetkaliyev

Rubagotti

2015

IEEE/ASME Trans. Mechatron.

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Abstract-This paper presents a framework for generating optimal motor trajectories for a spherical parallel manipulator (SPM) with revolute joints, actuated by servomotors with default internal position control settings. The proposed framework consists of three phases. First, an approach to obtain unique forward kinematics is introduced, in order to relate the angular positions of the servomotors to the orientation of the SPM top mobile platform. Then, a configuration space for the SPM is defined by using numerical procedures, in order to guarantee the absence of singularities and of collisions between links during the motion of the manipulator. Finally, reference trajectories of the servomotors are defined via convex optimization. These trajectories determine an optimal evolution of the SPM motion, based on configuration space and original servomotor dynamics. The proposed strategy is experimentally demonstrated on a prototype of Agile Wrist SPM with three servomotors.

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“…It has been shown in the literature (see refs. [6][7][8][9], for example) that the Agile Eye has a set of nonlinear inputoutput kinematic equations. Even though one may derive a formula that produces a unique current solution to the forward displacement analysis [9], the set of input-output kinematic equations of the Agile Eye is still nonlinear.…”

Section: Zhang and F Zhangmentioning

confidence: 99%

“…The solutions given in refs. [7,9] have been verified and implemented in the control of the Agile Eye in the Robotics Lab at Laval University, Canada. Accordingly, the linear relation in Eq.…”

Section: Zhang and F Zhangmentioning

confidence: 99%

Comments on “Design and analysis of a totally decoupled 3-DOF spherical parallel manipulator” by D. Zhang and F. Zhang (Robotica, Available on CJO 19 Nov, 2010, doi:10.1017/S0263574710000652)

2011

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D. Zhang and F. Zhang addressed the issue of designing and analyzing totally decoupled 3-DOF spherical parallel manipulators (SPMs) and concluded that the SPMs in Figs. 5(a) and 5(b) of ref. [1] are completely decoupled and fully isotropic (see Abstract, Section 5, and Conclusions in ref. [1]). This topic is of great interest to researchers working in the general area of parallel mechanisms. However, we disagree with the authors of ref. [1] on their conclusion.

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A Closed-Form Solution for the Direct Kinematics of a Special Class of Spherical Three-Degree-of-Freedom Parallel Manipulators

Cited by 28 publications

References 6 publications

An approach for obtaining unique kinematic solutions of a spherical parallel manipulator

An approach for obtaining unique kinematic solutions of a spherical parallel manipulator

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Comments on “Design and analysis of a totally decoupled 3-DOF spherical parallel manipulator” by D. Zhang and F. Zhang (Robotica, Available on CJO 19 Nov, 2010, doi:10.1017/S0263574710000652)

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