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.

scholarly journals Comparison of Planar Parallel Manipulator Architectures Based on a Multi-Objective Design Optimization Approach

2010 ◽  
Author(s):  
Damien Chablat ◽  
Ste´phane Caro ◽  
Raza Ur-Rehman ◽  
Philippe Wenger
Keyword(s):  
Genetic Algorithm ◽  
Design Optimization ◽  
Parallel Manipulator ◽  
Optimization Problem ◽  
Optimization Approach ◽  
Objective Functions ◽  
Multi Objective ◽  
Planar Parallel Manipulator ◽  
Moving Platform ◽  
Pareto Frontiers

This paper deals with the comparison of planar parallel manipulator architectures based on a multi-objective design optimization approach. The manipulator architectures are compared with regard to their mass in motion and their regular workspace size, i.e., the objective functions. The optimization problem is subject to constraints on the manipulator dexterity and stiffness. For a given external wrench, the displacements of the moving platform have to be smaller than given values throughout the obtained maximum regular dexterous workspace. The contributions of the paper are highlighted with the study of 3-PRR, 3-RPR and 3-RRR planar parallel manipulator architectures, which are compared by means of their Pareto frontiers obtained with a genetic algorithm.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

2004 ◽  
Vol 218 (7) ◽  
pp. 721-730 ◽  
Author(s):  
S Kemal Ider
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Full Rank ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dynamic Equations ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Pass Through ◽  
Full Utilization

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Wrench Capabilities of a Kinematically Redundant Planar Parallel Manipulator

Robotica ◽  
2021 ◽  
pp. 1-16
Author(s):  
Roger Boudreau ◽  
Scott Nokleby ◽  
Marise Gallant
Keyword(s):  
Explicit Solution ◽  
Parallel Manipulator ◽  
Maximum Force ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Force Analysis ◽  
Maximum Moment ◽  
Planar Parallel Manipulator

SUMMARY This paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

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.

The effects of joint clearance on the dynamics of the 3RRR planar parallel manipulator

Robotica ◽  
2016 ◽  
Vol 35 (6) ◽  
pp. 1223-1242 ◽  
Author(s):  
S. M. Varedi-Koulaei ◽  
H. M. Daniali ◽  
M. Farajtabar
Keyword(s):  
Parallel Manipulator ◽  
Dynamic Performance ◽  
Contact Forces ◽  
Force Model ◽  
Continuous Contact ◽  
Dissipative Term ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Performance Reduction ◽  
Design And Manufacturing

SUMMARYIn reality, clearances in the joints are inevitable due to tolerances, and defects arising from design and manufacturing. Therefore, poor dynamic performance, reduction in components component lifetimes and generation of undesirable vibrations result in impacts of mating parts in the clearance joint. In this study, the dynamic behavior of a planar mechanism with revolute joints, in the presence of clearances is investigated. A continuous contact force model, based on elastic Hertz theory together with a dissipative term, is used to evaluate the contact forces here. Moreover, using a contact model, the effects of working speed and clearance size on the dynamic characteristics of a planar mechanical system are analyzed and compared. Furthermore, numerical results for a 3RRR planar parallel manipulator with six revolute clearance joints are presented.

Contour Error of the 3-DoF Hydraulic Translational Parallel Manipulator

2014 ◽  
Vol 874 ◽  
pp. 57-62 ◽  
Author(s):  
Ryszard Dindorf ◽  
Piotr Wos
Keyword(s):  
Parallel Manipulator ◽  
Contour Error ◽  
Measuring Systems ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Directional Control ◽  
Fixed Base ◽  
Prismatic Joints ◽  
Hydraulic Cylinders ◽  
Tracking Trajectory

The paper deals with a selected problem of contour error for the desired tracking trajectory of the spatial 3-DoF hydraulic translational parallel manipulator (TPM). The prototype hydraulic TPM consists of a fixed base and a moving platform connected by the joints with three hydraulic linear axes. The closed-loop kinematic chains of the hydraulic TPM create a 3-RRPRR structure in which revolute joints R and prismatic joints P step out. The three equal integrated electro-hydraulic axes are prismatic joints P in which hydraulic cylinders are integrated with position measuring systems and proportional directional control valves.

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.

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