Dimensional Synthesis of Planar Parallel Manipulator Using Geared Linkages with Linear Actuation as Kinematic Chains

2016 ◽  
pp. 77-85
Author(s):  
S. M. Grigorescu ◽  
E.-C. Lovasz ◽  
D. T. Mărgineanu ◽  
C. Pop ◽  
F. Pop
Keyword(s):  
Parallel Manipulator ◽  
Dimensional Synthesis ◽  
Kinematic Chains ◽  
Planar Parallel Manipulator

Integrated optimal design of a high-speed planar parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 2976-2990 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
High Speed ◽  
Design Method ◽  
Tracking Error ◽  
Dimensional Synthesis ◽  
Tracking Accuracy ◽  
Nsga Ii ◽  
Parameters Tuning ◽  
Planar Parallel Manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

scholarly journals Accuracy Of Positioning And Orientation Of Effector Of Planar Parallel Manipulator 3RRR

2015 ◽  
Vol 9 (3) ◽  
pp. 151-154
Author(s):  
Monika Prucnal-Wiesztort
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Planar System ◽  
Kinematic Chains ◽  
Numerical Example ◽  
Advantages And Disadvantages ◽  
Planar Parallel Manipulator ◽  
Singular Configuration ◽  
Three Degrees Of Freedom

Abstract Parallel manipulator belongs to group of mechanisms with closed kinematic chains. This feature involves both advantages and disadvantages. The study examined the issue of accuracy of a planar system with three degrees of freedom, with revolute pairs, showing the effect of errors of the drives settings on effector positioning deviation. Enclosed is a numerical example for which analyzed the deviation in motion manipulator when going through the singular configuration. Based on the analysis was determined the area around the singular positions for which to obtain the orientation of the assumed accuracy is impossible.

Optimum force balancing of a planar parallel manipulator

2003 ◽  
Vol 217 (5) ◽  
pp. 515-524 ◽  
Author(s):  
G Alici ◽  
B Shirinzadeh
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Optimization Approach ◽  
Static Force ◽  
Force Analysis ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Motion Optimization ◽  
Balancing Conditions

This paper focuses on optimum force balancing of a planar parallel manipulator, articulated with revolute joints, with a combination of a proper distribution of link masses and two springs connected to the driving links. After conducting the static force analysis of the mechanism, the force balancing is formulated as an optimization problem such that a mean-square root of the sum-squared values of bearing and spring forces is minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of balancing conditions and the sizes of some inertial and geometric parameters are satisfied. The minimization of bearing forces and spring forces adds to the life of bearings and springs, transmits less shaking force and moment to the ground, decreases wear in the mechanism components and consequently reduces the actuation burden on the actuators when the manipulator is in motion. Optimization results indicate that the proposed optimization approach is systematic, versatile and easy to implement for the optimal balancing of the parallel manipulator and other kinematic chains.

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.

Geared Linkages with Linear Actuation Used as Kinematic Chains of a Planar Parallel Manipulator

2015 ◽  
pp. 21-31 ◽  
Author(s):  
Erwin-Christian Lovasz ◽  
Sanda Margareta Grigorescu ◽  
Dan Teodor Mărgineanu ◽  
Corina Mihaela Gruescu ◽  
Cristian Pop ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Chains ◽  
Planar Parallel Manipulator

Generation and Forward Displacement Analysis of RP_R-PR-RP_R Analytic Planar Parallel Manipulators

2002 ◽  
Vol 124 (2) ◽  
pp. 294-300 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Real Solutions ◽  
Planar Parallel Manipulator ◽  
Forward Displacement Analysis ◽  
Planar Parallel Manipulators

Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of RP_R-PR-RP_R analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of RP_R-PR-RP_R APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the RP_R-PR-RP_R planar parallel manipulator with two aligned platforms are given at the end of this paper.

Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing

Robotica ◽  
2004 ◽  
Vol 22 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Gürsel Alıcı ◽  
Bijan Shirinzadeh
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Kinematic Chains ◽  
Optimum Synthesis ◽  
Planar Parallel Manipulator ◽  
Distribution Parameters ◽  
Optimisation Procedure ◽  
Planar Parallel Manipulators

This paper deals with an optimum synthesis of planar parallel manipulators using two constrained optimisation procedures based on the minimization of: (i) the overall deviation of the condition number of manipulator Jacobian matrix from the ideal/isotropic condition number, and (ii) bearing forces throughout the manipulator workspace for force balancing. A revolute jointed planar parallel manipulator is used as an example to demonstrate the methodology. The parameters describing the manipulator geometry are obtained from the first optimisation procedure, and subsequently, the mass distribution parameters of the manipulator are determined from the second optimisation procedure based on force balancing. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum synthesis of the parallel manipulator and other kinematic chains. This work contributes to previously published work from the point of view of being a systematic approach to the optimum synthesis of parallel manipulators, which is currently lacking in the literature.

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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