Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

Ganesh, M.; Bihari, Banke; Rathore, V. S.; Kumar, Dhiraj; Kumar, C. Ramesh; Sree, Apelagunta Ramya; Sowmya, Karanam Naga; Dash, Anjan Kumar

doi:10.1017/s0263574716000710

Cited by 9 publications

(11 citation statements)

References 27 publications

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“…Results of the hypothesis test (μ A < μ B ) with a 5% significance for the optimization of a Delta parallel manipulator, with the objective functions described in Eqs. (8) and (10). function value (P control) for the first case than the EAs, but for the second case it cannot find a closed approximation to the EAs solution.…”

Section: Addressing the Problem Using A Quasi-newton Methodsmentioning

confidence: 99%

“…Searching for the best robot design and verifying that such design fulfills the system requirements is not a simple task for a human designer. As a consequence, there is a wide set of approaches, in the specialized literature, that intend to circumvent this issue by proposing algorithmic methodologies for automatic optimization for representative parallel kinematic structures like planar manipulators, 8,9 and spatial (3D) manipulators. [10][11][12][13] Design problems could be categorized by means of the order of the differential equations that have to be solved for simulating the robotic task, since it is directly related with the complexity of the problem and the task requirements.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The length of an edge of the cubic workspace is denoted by 2l and it is used to compute the objective function in Eq. (8). The center of the resultant maximal effective regular workspace is unknown for the evaluation of each candidate solution, but it is known that the manipulator is symmetrical with respect to the z-axis.…”

Section: Evaluation Of a Candidate Solutionmentioning

confidence: 99%

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Evaluating concurrent design approaches for a Delta parallel manipulator

Botello-Aceves¹,

Valdez²,

Becerra³

2018

Robotica

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SUMMARYThis paper addresses the problem of optimal mechanisms design, for the geometric structure and control parameters of mechanisms with complex kinematics, which is one of the most intricate problems in contemporary robot modeling. The problem is stated by means of task requirements and performance constraints, which are specified in terms of the end-effector's position and orientation to accomplish the task. Usually, this problem does not fulfill the characteristics needed to use gradient-based optimization algorithms. In order to circumvent this issue, we introduce case studies of optimization models using evolutionary algorithms (EAs), which deal with the concurrent optimization of both: structure and control parameters. We define and review several optimization models based on the workspace, task and dexterity requirements, such that they guarantee an adequate performance under a set of operating and joint constraints, for a Delta parallel manipulator. Then, we apply several methodologies that can approximate optimal designs. Additionally, we compare the EAs with a quasi-Newton method (the BFGS), in order to show that the last kind of methods is not capable of solving the problem if the initial point is not very close to a local optimum. The results provide directions about the best state-of-the-art EA for addressing different design problems.

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Section: Addressing the Problem Using A Quasi-newton Methodsmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Evaluation Of a Candidate Solutionmentioning

confidence: 99%

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Evaluating concurrent design approaches for a Delta parallel manipulator

Botello-Aceves¹,

Valdez²,

Becerra³

2018

Robotica

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“…So far, research into the kinematics of 3-RRR PPM is gradually developing from research on forward and reverse solution modeling based on rigid body kinematics to research on modeling the quasi-static response of planar flexure-hinge mechanisms using the new pseudo-rigid-body model of flexure hinges [5], or research on the motion reliability analysis of a 3-RRR PPM with multiple uncertainties, which include manufacturing tolerances, input errors, and joint clearances [6]. Furthermore, dynamics analysis [4], and workspace and singularity analysis [7][8][9][10][11][12] of the manipulator have also attracted the wide attention of scholars.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding 3-RRR PPM, although the geometric approach can determine the workspace area and analyze the relations between the geometrical parameters and workspace shapes, it cannot determine the singular points in workspace [7,8].…”

Section: Introductionmentioning

confidence: 99%

Small-angle perturbation method for moving platform orientation to avoid singularity of asymmetrical 3-RRR planner parallel manipulator

Yin

Chen

Gao

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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To overcome the weakness of the present methods of singularity avoidance for 3-RRR planar parallel manipulator (PPM), a new method of avoiding singular points on planed paths in workspace via orientation perturbation to moving platforms is proposed. First, an inverse kinematics model of 3-RRR PPM is built. A discriminant matrix of type II singularity is specified and the mapping between determinant values of the matrix and points in workspace of 3-RRR PPM is defined as a singularity surface. Then, the planned path is regarded as a directrix and intersecting line between cylindrical surfaces (its generating line is parallel to the z-axis) and the singularity surface is defined as a singularity curve corresponding to a planned path. By determining the critical perturbation value of the moving platform's orientation angle, the maximum value of the singularity curve corresponding to the planned path is no larger than 0 or its minimum value is no smaller than 0. Therefore, singular points on the planned path are avoided by changing the moving platform's orientation angle without changing the planned path. Moreover, a numerical realization method is given; example and experiment verification indicates that singular points in the planned path can be avoided when perturbation to the moving platform's orientation angle is no larger than 0.1745 rad. Therefore, the proposed method lays a solid foundation for singularity-free kinematics control based on inverse solutions.

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