A new geometric method for singularity analysis of spherical mechanisms

Zarkandi, Soheil

doi:10.1017/s0263574711000385

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…Now, vectors pro,1 v i and rotation matrix R pro,1 in equations ( 23), (25), and (28) are known, and we can compute values of vectors v i by the following relation…”

Section: Forward Position Kinematicsmentioning

confidence: 99%

“…In singular configurations, a parallel manipulator will gain or lose one or more instantaneous DOFs, 25,35 which leads to a loss of the controllability. Thus, singularity analysis is an essential step for design and control purposes of manipulators.…”

Section: Singularity Analysismentioning

confidence: 99%

“…Note that a curved prismatic joint connecting two links is also a revolute joint whose axis is perpendicular to the motion curve, the links move on it. 25 The most well-known SPM of this class is 3-RRR SPM (or 3-RRR Agile Wrist) studied extensively by Gosselin et al [8][9][10][11] Some SPMs with different architectures were also proposed in the literature. However, the literature is so limited.…”

Section: Introductionmentioning

confidence: 99%

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Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

Zarkandi

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper introduces a novel three degree-of-freedom spherical parallel manipulator with 3-PRR topology, where P and R denote a curved prismatic joint and a revolute joint, respectively. The first revolute joint of each PRR leg is actuated via a double Rzeppa-type driveshaft, and hence underlined. The manipulator has at most eight working modes and eight assembly modes. However, only one working mode and one assembly mode of the manipulator are acceptable during its motion which can be easily identified. Singularity and kinematic dexterity analyses reveal that the proposed 3-PRR spherical parallel manipulator has no forward kinematic singularity for a wide range of rotation of the moving platform around its central axis. An optimal design of the manipulator is also presented having a workspace with good kinematic dexterity.

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“…Now, vectors pro,1 v i and rotation matrix R pro,1 in equations ( 23), (25), and (28) are known, and we can compute values of vectors v i by the following relation…”

Section: Forward Position Kinematicsmentioning

confidence: 99%

Section: Singularity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

Zarkandi

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…By means of the two Jacobian matrices, researchers have analyzed the singulariy of many types of mechanisms, such as planar manipulators, 16,36 serial manipulators, 37 and spatial parallel manipulators. 35,[38][39][40][41][42][43] Besides, Di Gregorio 44 and Zarkandi 45 represented geometric methods to analyze the singularity of planar and spherical parallel mechanisms. However, there are no studies, to the authors' knowledge, addressing the singularity analysis of spatial multi-loop mechanisms with coupled closed chains, such as the Hoberman switch-pitch ball, 1 magic balls, 2 magic cubes, 3 and the DTMLM.…”

Section: Introductionmentioning

confidence: 99%

Mobility and singularity analyses of a symmetric multi-loop mechanism for space applications

Ángeles

Guo

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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A symmetric, double-tripod multi-loop mechanism (DTMLM), for aerospace applications, is the subject of this paper. Its mobility and singularity are analyzed, while introducing a novel tool, the cell-division method for singularity analysis, applicable to multi-loop mechanisms. The key principle of this method lies in replacing the singularity analysis of the original multi-loop mechanism with: (1) that of an equivalent simpler parallel mechanism; (2) the constraint analysis between loops; and (3) the singularity analysis of simpler kinematic subchains. Then, the mechanism is transformed into a simpler, equivalent parallel mechanism with three identical kinematic subchains. Its mobility and singularity are analyzed based on screw algebra, which leads to a key conclusion about the geometric properties of this mechanism. Results show that: (a) the DTMLM has three degrees of freedom (dof), i.e., two rotational dof around two intersecting axes lying in the middle plane of the mechanism, and one translational dof along the normal to the said plane (2R1T); and (b) the singularities of the 3-RSR parallel mechanism are avoided in the DTMLM by means of prismatic joints, singularities in the DTMLM occurring on the boundary of its workspace. Thus, the DTMLM has a 2R1T mobility everywhere within its workspace. When a set of multi-loop mechanisms of this kind are stacked as modules to assemble a multi-stage manipulator for space applications, the modules can be designed so that, under paradigm operations, all individual loops operate within their workspace, safe from singularities.

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“…Moreover, it can handle, single or multi-loop kinematic chains regardless if they are determined or undetermined, even exceptional and paradoxical linkages, see Hervé (1978). Some applications of the instantaneous screw axes, or their counterparts, in the case of planar and spherical linkages, can be found in Zhao and Zhou (2004), Di Gregorio (2007) and Zarkandi (2011).…”

Section: Introductionmentioning

confidence: 99%

A general method for the determination of the instantaneous screw axes of one-degree-of-freedom spatial mechanisms

2020

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Abstract. This contribution shows that a method proposed previously, for the determination of the instantaneous centers of rotation of planar closed chains, can be generalized for the determination of the instantaneous screw axes of general one-degree-of-freedom spatial mechanisms. Hence, the approach presented in this paper can be applied to any of the closed chains that belong to any of the subgroups of the Euclidean group, SE(3), namely planar, spherical or chains associated with the Schönflies subgroups, among others. Furthermore it can be also applied to multi-loop mechanisms and even to closed chains that are exceptional o paradoxical, as indicated by Hervé.

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A new geometric method for singularity analysis of spherical mechanisms

Cited by 13 publications

References 14 publications

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

Mobility and singularity analyses of a symmetric multi-loop mechanism for space applications

A general method for the determination of the instantaneous screw axes of one-degree-of-freedom spatial mechanisms

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