A family of spherical parallel manipulators with two legs

Gallardo, Jaime; Rodríguez, Ramón López; Caudillo, Martín; Rico, José M.

doi:10.1016/j.mechmachtheory.2007.02.001

Cited by 28 publications

(12 citation statements)

References 30 publications

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“…This completes the solution of the inverse kinematics problem. Next, with the known v k and w k from robot structure and calculated γ k from the inverse kinematics problem, we can obtain the unit vectors r k using (15). These unit vectors, r k , are needed to obtain the velocity and acceleration Jacobian matrices.…”

Section: Inverse Kinematics Analysismentioning

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: Inverse Kinematics Analysismentioning

confidence: 99%

“…Moreover, Di Gregorio [10] proposed a non-overconstrained SPM composed of three RRS-type legs. Also, Gallardo et al [15] proposed a family of spherical parallel manipulators with a compact asymmetrical topology consisting of two legs and one spherical joint.…”

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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“…Analogous concepts were used to design non-redundant PKM with decoupled rotational and translational motion [33] and 2D orientating mechanisms [34,35]. One example of the second class is the 3-DOF 3SPS/S that is presented in [8][9][10][11], which has three legs with spherical-prismatic-spherical-joints and one additional spherical joint connecting the mobile platform to the fixed base.…”

Section: Introductionmentioning

confidence: 99%

“…Analogous concepts were used to design non-redundant PKM with decoupled rotational and translational motion [33] and 2D orientating mechanisms [34,35]. The concept of projective angles has been introduced by [36] and represents a useful approach for the kinematic analysis of PKMs.…”

Section: Introductionmentioning

confidence: 99%

Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

Legnani

Fassi

2018

Robotics

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This paper presents the kinematics analysis of a class of spherical PKMs Parallel Kinematics Machines exploiting a novel approach. The analysis takes advantage of the properties of the projective angles, which are a set of angular conventions of which their properties have only recently been presented. Direct, inverse kinematics and singular configurations are discussed. The analysis, which results in the solution of easy equations, is developed at position, velocity and acceleration level.

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“…14 Gallardo et al. 15 investigated a family of nonoverconstrained SPMs consisting of one passive spherical joint and two limbs. Mohammadi et al.…”

Section: Introductionmentioning

confidence: 99%

Design and kinematic analysis of a spherical parallel manipulator using concurrent planar parallelogram linkages

Chen

Wang

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents the design of a novel spherical parallel manipulator. The spherical parallel manipulator consists of three identical limbs and each of them is formed by a planar parallelogram linkage, a universal joint, and a revolute one, successively. Its mobility is analyzed using the reciprocal screws. After that, the kinematics is analyzed in detail, including inverse kinematic modeling, which is validated by a numerical example, inverse Jacobian analysis, singularity analysis, and manipulability analysis, which shows a relatively good performance of force transmission. Then based on the analysis, one prototype is fabricated to validate the effectiveness and feasibility of the design. In the end, some conclusions are drawn and future works are discussed.

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A family of spherical parallel manipulators with two legs

Cited by 28 publications

References 30 publications

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

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

Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

Design and kinematic analysis of a spherical parallel manipulator using concurrent planar parallelogram linkages

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