Precise Stiffness and Elastic Deformations of Serial–Parallel Manipulators by Considering Inertial Wrench of Moving Links

Robotica ◽  
2020 ◽  
Vol 38 (12) ◽  
pp. 2204-2220
Author(s):  
Yi Lu ◽  
Zhuohong Dai ◽  
Yang Lu
Keyword(s):  
Elastic Deformation ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Elastic Deformations ◽  
In Series ◽  
Deformation Models

SUMMARYA general serial–parallel manipulator connected in series by two different parallel manipulators with linear active legs is constructed. Its precise stiffness and elastic deformations are studied systematically. Its unified precise stiffness and precise elastic deformation models are established by considering both the moving links inertial wrench and the dynamic active/constrained wrench. A 3SPR+3RPS-type serial–parallel manipulator is illustrated for solving its precise stiffness and precise elastic deformation. The derived formulae of the precise stiffness and the precise elastic deformations of the general serial–parallel manipulator are verified by the theoretical solutions of the 3SPR+3RPS serial–parallel manipulator.

Solving elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry

2013 ◽  
Vol 227 (12) ◽  
pp. 2810-2824 ◽  
Author(s):  
Yi Lu ◽  
Cong Cong ◽  
Chen Liwei ◽  
Peng Wang
Keyword(s):  
Elastic Deformation ◽  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Elastic Deformations ◽  
Deformation Equation ◽  
Computer Aided ◽  
Force Transformation ◽  
Design Variation ◽  
Aided Design

It has been a significant and challenging issue to determine the elastic deformation of parallel manipulators for their precision analysis and control. A new method is proposed and studied for solving the elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry. First, an original simulation mechanism of a parallel manipulator is constructed; each of the vectors in the force transformation matrix of the parallel manipulators is constructed by this simulation mechanism. The active/constrained wrench and their pose are determined based on the Newton–Euler formulation. Second, the elastic deformed dimensions of the active legs are determined based on the elastic deformation equation and the active/constrained wrench. Third, a new simulation mechanism of this parallel manipulator is constructed by replacing the original dimensions of active legs with the deformed dimensions of active legs and the elastic deformations of parallel manipulators are solved using the pose difference between the original and new simulation mechanisms. Finally, two parallel manipulators are illustrated and their elastic deformations are solved and verified by both analytic approach and finite element method.

Direct Position Analysis in Analytical Form of Parallel Manipulators Generating Structures With Topology SR-2PS

2004 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Solution Procedure ◽  
Generic Structure ◽  
Kinematic Chains ◽  
Position Analysis ◽  
In Series ◽  
The One ◽  
Wide Family

A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. One out of these topologies is the SR-2PS topology (one SR leg and two PS legs). This paper presents an algorithm that determines all the assembly modes of the structures with topology SR-2PS in analytical form. The presented algorithm can be applied without changes to solve, in analytical form, the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked. In particular, the closure equations of a generic structure with topology SR-2PS are written. The eliminant of this system of equations is determined and the solution procedure is presented. Finally, the proposed procedure is applied to a real case. This work demonstrates that the solutions of the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked are at most eight.

scholarly journals Stiffness and Elastic Deformation of 4-DoF Parallel Manipulator with Three Asymmetrical Legs for Supporting Helicopter Rotor

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jialin Song ◽  
Yang Lu ◽  
Yongli Wang ◽  
Yi Lu
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Elastic Deformation ◽  
Stiffness Matrix ◽  
Parallel Manipulator ◽  
Element Model ◽  
Helicopter Rotor ◽  
Elastic Deformations ◽  
The Finite Element Model ◽  
Type Composite

The stiffness and elastic deformation of a 4-DoF parallel manipulator with three asymmetrical legs are studied systematically for supporting helicopter rotor. First, a 4-DoF 2SPS + RRPR type parallel manipulator with two linear SPS type legs and one RRPR type composite leg is constructed and its constraint characteristics are analyzed. Second, the formulas for solving the elastic deformation and the stiffness matrix of the above mentioned three asymmetrical legs are derived. Third, the formulas for solving the total stiffness matrix and the elastic deformation of this manipulator are derived and analyzed. Finally, its finite element model is constructed and its elastic deformations are solved using both the derived theoretical formulas and the finite element model. The theoretical solutions of the elastic deformations are verified by that of the finite element model.

Accuracy Analysis Considering Clearances and Elastic Deformations in Parallel Manipulators

2011 ◽  
Author(s):  
Jokin Aginaga ◽  
Oscar Altuzarra ◽  
Erik Macho ◽  
Jon Olza
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Linear Analysis ◽  
Accuracy Analysis ◽  
Elastic Deformations ◽  
End Effector ◽  
Planar Mechanism ◽  
General Methodology ◽  
Pick And Place ◽  
Mechanical Components

Clearances at joints and deformability of links produce a loss of accuracy when positioning a mechanism. End-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances and the rigidity of the mechanical components. Clearance magnitudes and elastic deformations are much smaller than other dimensions and consequently they are assumed to be infinitesimal, which leads to a linear analysis. Under this assumption, velocity equations can be utilized instead of position ones, and they can be easily expressed by using screw coordinates. A general methodology for analyzing the pose accuracy of a parallel manipulator is presented, making use of the example of a 5R planar mechanism along a pick-and-place trajectory.

Statics and Stiffness Model of Serial-Parallel Manipulator Formed by k Parallel Manipulators Connected in Series

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Bo Hu ◽  
Jingjing Yu ◽  
Yi Lu ◽  
Chunping Sui ◽  
Jianda Han
Keyword(s):  
Theoretical Basis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Serial Manipulators ◽  
Stiffness Model ◽  
In Series

The statics and stiffness model of serial-parallel manipulators (S-PMs) formed by k parallel manipulators (PMs) connected in series is established in this paper. The S-PMs can provide features of both serial manipulators (SMs) and PMs. First, the unified formulae for solving the statics and stiffness of S-PMs are derived. Second, a k(PS + RPS + SPS) S-PM is analyzed to illustrate this model. Finally, an analytic solved example for 5(PS + RPS + SPS) S-PM is given. The established model can offer an essential theoretical basis for S-PMs.

Analyses of the stiffness and elastic deformation of a 2(3-SPR) serial—parallel manipulator

2009 ◽  
Vol 223 (3) ◽  
pp. 189-198 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Elastic Deformation ◽  
Machine Tools ◽  
Parallel Manipulator ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Robot Arm ◽  
Principle Of Virtual Work ◽  
Compliance Matrix ◽  
End Effector ◽  
Machining Speed

Stiffness is one of the important indices for evaluating the performances of serial—parallel manipulators (S—PMs), particularly when the S—PMs are used as machine tools and the robot arm/leg, and higher stiffness allows higher machining speed with higher accuracy of the end-effector. In this article, the stiffness and the elastic deformation of a 2(3-SPR) S—PM are studied systematically. First, a 2(3-SPR) S—PM, including an upper 3-SPR parallel manipulator (PM) and a lower 3-SPR PM, is constructed, and its characteristics are analysed. Second, some formulae for solving the elastic deformation and the compliance matrix of the active legs are derived from the available kinematics/statics of this S—PM. Third, based on the principle of virtual work and the compliance matrix of the active legs, the elastic deformation and the total stiffness matrix of this S—PM are solved and analysed.

Assessing Position Error Due to Clearances and Deformations of Links in Parallel Manipulators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Jokin Aginaga ◽  
Oscar Altuzarra ◽  
Erik Macho ◽  
Xabier Iriarte
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Position Error ◽  
Elastic Deformations ◽  
End Effector ◽  
Pick And Place ◽  
Smooth Movement ◽  
Mechanical Components

Two of the main sources of position error in parallel manipulators are clearances at joints and elastic deformations of the links. The former are usually necessary in order to produce a smooth movement between the pin and the hub of a joint. The latter are unavoidable and they tend to be greater in manipulators designed for pick-and-place tasks due to the need of light links. It can be stated that the end-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances, and the rigidity of the mechanical components. This paper proposes a procedure to calculate position error in parallel manipulators due to both clearances and elastic deformations. Although the procedure is applicable to any planar or spatial parallel manipulator, a planar 5R mechanism is used as an illustrative example in order to make it easier to understand.

The study of the elastic deformation of a flexible wheel by a cam wave generator

2020 ◽  
Vol 65 (1) ◽  
pp. 51-58
Author(s):  
Sava Ianici
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Theoretical Study ◽  
Elastic Field ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Wave Generator ◽  
Two Stages

The paper presents the results of research on the study of the elastic deformation of a flexible wheel from a double harmonic transmission, under the action of a cam wave generator. Knowing exactly how the flexible wheel is deformed is important in correctly establishing the geometric parameters of the wheels teeth, allowing a better understanding and appreciation of the specific conditions of harmonic gearings in the two stages of the transmission. The veracity of the results of this theoretical study on the calculation of elastic deformations and displacements of points located on the average fiber of the flexible wheel was subsequently verified and confirmed by numerical simulation of the flexible wheel, in the elastic field, using the finite element method from SolidWorks Simulation.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

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