Considering the Ability for Nonsingular Transitions of Assembly Mode for Dimensional Synthesis

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Vi´ctor Petuya ◽  
Mo´nica Uri´zar ◽  
Alfonso Herna´ndez
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Complex Singularity ◽  
Algebraic Expressions ◽  
Free Region ◽  
Dimensional Parameters ◽  
Cusp Points ◽  
Singularity Locus

An important difficulty in the design of parallel manipulators is their reduced practical workspace, due mainly to the existence of a complex singularity locus within the workspace. The workspace is divided into singularity-free regions according to assembly modes and working modes, and the dimensioning of parallel manipulators aims at the maximization of those regions. It is a common practice to restrict the manipulator’s motion to a specific singularity-free region. However, a suitable motion planning can enlarge the operational workspace by means of transitions of working mode and/or assembly mode. In this paper, the authors present an analytical procedure for obtaining the loci of cusp points of a parallel manipulator as algebraic expressions of its dimensional parameters. The purpose is to find an optimal design for non-singular transitions to be possible.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

Optimal Design of a Planar Five-Bar Parallel Manipulator Driven by Two Orthogonal Layout Actuators

2012 ◽  
Vol 490-495 ◽  
pp. 2681-2685
Author(s):  
Xiao Rong Zhu ◽  
Yi Lu ◽  
Hui Ping Shen
Keyword(s):  
Parallel Manipulator ◽  
Good Condition ◽  
Parallel Manipulators ◽  
Condition Index ◽  
Link Length ◽  
Geometry Design ◽  
Dimensional Parameters ◽  
Linear Actuators ◽  
Basic Good

This paper addresses geometry design of a new kind of 2-DOF five-bar parallel manipulator actuated by two orthogonal layout linear actuators. Although the manipulator has only one geometric parameter, i.e., the link length, the distribution of performance index is more complex. Here, we propose a design approach utilizing a performance chart and local condition index. The key problem in the design of the manipulator is the determination of not the link length but the workspace satisfying the design index. This paper gives an effective method to obtain the basic good-condition workspace without dimension. Then, based on the optimum non-dimensional result, the optimum dimensional parameters are achieved which is suitable for the desired workspace. The optimum methodology of this paper is convenient and can be extended to other parallel manipulators

Pareto-Optimal Solutions Using Kinematic and Dynamic Functions for a Scho¨nflies Parallel Manipulator

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Charles Pinto ◽  
Bogdan Sandru ◽  
Enrique Amezua
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Frobenius Norm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Motion Generation ◽  
Dimensional Parameters

The search of Pareto-optimal solutions for the optimal design of Low-Mobility Parallel Manipulators with Scho¨nflies motion is the subject of this paper. As a working example, a four-degree-of-freedom symmetric parallel manipulator for Scho¨nflies-motion generation is taken. In previous work, analytically found objective functions for the optimal design were used. As a consequence, some limitations were detected and new functions are required. First, a manipulator description is made, and kinematic and dynamic problems are solved. Next, an operational and dexterous workspace along with its volume is found making use of a discretization. Further, the variation of this volume with dimensional parameters is shown for purpose of optimal design. Similarly, the manipulator’s dexterity based on the Frobenius norm is found and weighted with the measure of dispersion. Then, upon a type of testing trajectory over this workspace, kinematic and dynamic results in the actuators are proposed as objective functions in multiobjective optimization.

Optimal Design of Spherical 5R Parallel Manipulators Considering the Motion/Force Transmissibility

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Chao Wu ◽  
Xin-Jun Liu ◽  
Liping Wang ◽  
Jinsong Wang
Keyword(s):  
Performance Evaluation ◽  
Optimal Design ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Force Transmission ◽  
Minimally Invasive Surgical ◽  
Pointing Device ◽  
Force Transmissibility

The spherical 5R parallel manipulator is a typical parallel manipulator. It can be used as a pointing device or as a minimally invasive surgical robot. This study addresses the motion/force transmission analysis and optimization of the manipulator by taking into account the motion/force transmissibility. The kinematics of the manipulator is analyzed. Several transmission indices are defined by using screw theory for the performance evaluation and dimensional synthesis. The process of determining the optimal angular parameters based on performance charts is presented. The manipulator that has a large workspace and good motion/force transmissibility is identified.

A Task Driven Approach to Simultaneous Type Synthesis and Dimensional Optimization of Planar Parallel Manipulator Using Algebraic Fitting of a Family of Quadrics

2013 ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Q. J. Ge ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Surface Fitting ◽  
Image Space ◽  
Synthesis Process ◽  
Dimensional Synthesis ◽  
Planar Parallel Manipulator ◽  
Kinematic Mapping ◽  
The Given

This paper studies the rigid body guidance problem for 3-DOF planar parallel manipulators (PPM) with three-triad assembly. We present a novel, unified, and simultaneous type and dimensional synthesis approach to planar parallel manipulator synthesis by using kinematic mapping, surface fitting, and least squares techniques. Novelty of our approach lies in linearization of a highly non-linear problem and the fact that the nature of the given motion or displacement drives the synthesis process without assuming triad topology or their geometry. It has been well established that by using planar quaternions and kinematic mapping, workspace related constraints of planar dyads or triads can be represented as algebraic constraint manifolds in the image space of planar displacements. The constraints associated with planar RR-, PR- and RP-dyads correspond to a single quadric in the image space, while that of each of the six planar triads (RRR, RPR, PRR, PPR, RRP and RPP) map to a pair of quadrics and the space between them. Moreover, the quadrics associated with RRR- and RPR-triads are of the same type as that of RR dyads, of PRR- and PPR-triads as that of PR-, and RRP- and RPP-triads as that of RP-dyad. This simplification nicely extends a dyad synthesis problem to a triad synthesis one. The problem is formulated as the least-squares error minimization problem to find a trinity of quadrics that best fit the image points of task displacements. The fitting error corresponding to each single quadric of the trinity is regarded as variation (thickness) of that quadric, which turns that quadric into a pair of quadrics. Hence, three dyads with minimal surface fitting errors can be converted to three triads in the Cartesian space.

Designing a Translational Parallel Manipulator Based on the 3SS Kinematic Joint

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Alfonso Hernández
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Modular Design ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Point Of View ◽  
Pick And Place ◽  
Prismatic Joints ◽  
Singularity Locus ◽  
Kinematic Joint

Abstract Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

Analytical Procedure Based on the Matrix Structural Method for the Analysis of the Stiffness of the 2PRU–1PRS Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (08) ◽  
pp. 1401-1414
Author(s):  
Saioa Herrero ◽  
Charles Pinto ◽  
Mikel Diez ◽  
Javier Corral
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Shaking Table ◽  
Structural Method ◽  
Positioning Accuracy ◽  
Serial Manipulators ◽  
Kinematic Chains ◽  
Workspace Analysis ◽  
The Matrix

SummaryParallel manipulators, especially those with outputs as one translation and two rotations (1T2R), are being increasingly studied. The kinematic chains of parallel manipulators share the loads and make the stiffness higher than the stiffness of serial manipulators with equivalent limbs. This high stiffness ensures a minimal deformation of the limbs, allowing a high positioning accuracy of the endeffector. Thus, it is very important to be able to measure the stiffness in parallel manipulators. In this work, we present a novel 1T2R multi-axial shaking table (MAST) for automobile pieces testing purposes—the 2PRU–1PRS parallel manipulator—and focus on the analysis of its stiffness all over the useful workspace. Analysis methods based on matrix structural method need to be validated for every parallel manipulator, and we present these steps along with a comparison between experimental and analytical methods.

Mobility analysis and kinematic synthesis of a novel 4-DoF parallel manipulator

Robotica ◽  
2014 ◽  
Vol 34 (5) ◽  
pp. 1010-1025 ◽  
Author(s):  
Gang Dong ◽  
Tao Sun ◽  
Yimin Song ◽  
Hao Gao ◽  
Binbin Lian
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Screw Theory ◽  
Programming Approach ◽  
The Novel ◽  
Dimensional Synthesis ◽  
Vector Method ◽  
Dimensional Parameters ◽  
Design And Manufacture

SUMMARYThis paper proposes a novel parallel manipulator with 1 translational and 3 rotational degrees of freedom, which may be designed as the docking equipment for large-scale component assemblage in the aircraft industry. First, the mobility and kinematic analysis of the novel manipulator is performed using the screw theory and the closed-loop vector method. To evaluate the kinematic performance of the manipulator, its workspace is calculated, and the dimensional homogeneous Jacobian matrix of this manipulator is deduced. Mainly based on a nonlinear programming approach, the kinematic dimensional synthesis is performed to optimise the dimensional parameters of this novel parallel manipulator in a prescribed workspace. The results of this paper may lay a solid foundation for the prototype design and manufacture of the novel parallel manipulator.

A novel planar parallel manipulator with high orientation capability for a hybrid machine tool: kinematics, dimensional synthesis and performance evaluation

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1031-1053 ◽  
Author(s):  
Samy F. M. Assal
Keyword(s):  
Performance Evaluation ◽  
Machine Tool ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Hybrid Machine ◽  
High Orientation

SUMMARYIn order to potentially realize the advantages of planar parallel manipulators to be used for hybrid machine tools, the inherently abundant singularities which diminish the usable workspace must be eliminated. Proper structure synthesis and dimensional synthesis can provide a good solution. So, a non-conventional architecture of a three-PPR planar parallel manipulator is proposed in this paper for a hybrid machine tool. The proposed architecture permits a large dexterous workspace with unlimited orientation capability and no singularities. It also provides partially decoupled motion which permits independent actuators control. The kinematic, singularity, orientation capability and workspace analyses of the proposed manipulator are studied to verify those advantages. Based on a non-dimensional design parameter space, the highly important indices for this application namely the workspace index (WI), the motion/force transmission index, the kinematic and dynamic dexterity indices and the stiffness index are selected to be maximized yielding proper dimensions of the design parameters. Those performance indices are proven to be uniform over all the workspace achieving highly important characteristics of uniform accuracy, acceleration characteristics, rigidity and force transmissibility. Performance evaluation is finally presented to verify the high performance of the proposed non-singular planar parallel manipulator with high orientation capability.

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