A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Donghao Yang
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Fea Model ◽  
Stiffness Model ◽  
Compliance Modeling ◽  
The One

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

Kinetostatics Modeling and Decoupling Analysis of a Crosshair Flexures-Based Nanopositioner

2017 ◽  
Author(s):  
Pengbo Liu ◽  
Songsong Lu ◽  
Peng Yan ◽  
Zhen Zhang
Keyword(s):  
Performance Improvement ◽  
Open Loop ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Input And Output ◽  
Stiffness Model ◽  
Decoupling Analysis ◽  
Compliance Matrix Method ◽  
Cross Axis ◽  
Castigliano’S Theorem

In the present paper, we take the input and output decoupling into account and propose a 2-DOF parallel nanopositioner, which is composed of lever amplification mechanisms, compound parallelogram mechanisms and novel crosshair flexures. In order to demonstrate the decoupling performance improvement of the crosshair flexures, the stiffness model of the crosshair flexures and the kinetostatics model of the nanopositioner are established based on Castigliano’s theorem and the compliance matrix method. Accordingly, the input and output decoupling compliance matrix models are derived to demonstrate the excellent decoupling property of the crosshair flexures based nanopositioner, which is further verified by finite-element analysis and experimental results. The open-loop experiments on the prototype stage demonstrate the maximum stroke of the nanopositioner is up to 65μm and the cross axis coupling errors are less than 1.6%.

Kinematic analyses of novel translational parallel manipulators

2013 ◽  
Vol 228 (2) ◽  
pp. 330-341 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Horacio Orozco-Mendoza ◽  
Alvaro Sánchez-Rodríguez ◽  
Gursel Alici
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Output Displacement ◽  
Kinematic Analyses ◽  
Linear Actuators ◽  
The One ◽  
Forward Kinematic ◽  
Primary Contribution

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

Approximate Stiffness Modelling and Stiffness Defect Identification for a Heavy-load Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (6) ◽  
pp. 1120-1142 ◽  
Author(s):  
Shuai Fan ◽  
Shouwen Fan
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Contact Deformation ◽  
Heavy Load ◽  
Compliance Matrix ◽  
Defect Identification ◽  
Clearance Joint ◽  
Stiffness Model ◽  
Joint Contact

SummaryWhen using parallel manipulators as machine tools, their stiffness is an important factor in the quality of the produced products. This paper presents an overall approximate stiffness model for a heavy-load parallel manipulator, which considers the effects of actuator stiffness, joint clearance, joint contact deformation, and limb deformation. Based on the principle of virtual work and the introduced modified parameters, the proposed overall compliance matrix successfully takes four factors into a unified expression. To obtain the overall compliance matrix, the approximate stiffness models of the joint clearance, joint contact deformation, and limb deformation are given. In addition, by combining the statistical simulation including the random uncertainties and the proposed approximate stiffness models as the basis of the magnitudes for each random variable, an approach based on the expected trajectory and external load is also proposed for stiffness defect identification such that the estimation is more accurate and reliable. Finally, a numerical example of the 1PU+3UPS parallel manipulator and a discussion are presented to demonstrate the practicability of the proposed stiffness model and defect identification approach. After modifying the structure parameters of the defective components, the prototype experiences a significant stiffness improvement.

Analytical Elastostatic Stiffness Modeling of Overconstrained Parallel Manipulators Using Geometric Algebra and Strain Energy

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Qinchuan Li ◽  
Lingmin Xu ◽  
Qiaohong Chen ◽  
Xinxue Chai
Keyword(s):  
Geometric Algebra ◽  
Strain Energy ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Outer Product ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Stiffness Matrices

A general method for the analytical elastostatic stiffness modeling of overconstrained parallel manipulators (PMs) using geometric algebra and strain energy is proposed. First, an analytical solution of the constraint and actuation wrenches exerted on the moving platform is obtained using the outer product and dual operation of geometric algebra, which avoids solving complex symbolic linear equations. Second, considering the compliances of the limbs, an analytical elastostatic model is established using the strain energy to obtain the stiffness matrices of the limbs. Finally, the deformation compatibility equations are added into equilibrium equations to obtain the overall stiffness matrix of the PM, which has a concise expression and a clear physical meaning. The proposed method is applied to the Tex3 overconstrained PM and the Tex4 overconstrained PM with redundant actuation to prove its validity. Comparable results between the theoretical analysis and the finite-element analysis (FEA) show that the former could be used as an effective alternative to the FEA method in the predesign stage. This new approach is universally applicable to the elastostatic stiffness analysis of overconstrained PMs.

scholarly journals Design of Four-DoF Compliant Parallel Manipulators Considering Maximum Kinematic Decoupling for Fast Steering Mirrors

Actuators ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 292
Author(s):  
Guangbo Hao ◽  
Haiyang Li ◽  
Yu-Hao Chang ◽  
Chien-Sheng Liu
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Laser Beams ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Precision Control ◽  
Motion System ◽  
Matrix Modelling

Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify high-precision control in parallel manipulators, maximum kinematic decoupling is always desired. A constraint map method is used to propose the four required DoF with the consideration of maximum kinematic decoupling. A specific compliant mechanism is presented based on the constraint map, and its kinematics is estimated analytically. Finite element analysis demonstrates the desired qualitative motion and provides some initial quantitative analysis. A normalization-based compliance matrix is finally derived to verify and demonstrate the mobility of the system clearly. In a case study, the results of normalization-based compliance matrix modelling show that the diagonal entries corresponding to the four DoF directions are about 10 times larger than those corresponding to the two-constraint directions, validating the desired mobility.

Constraint-Force-Based (CFB) Modeling of Compliant Mechanisms

2015 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Static Equilibrium ◽  
Constraint Forces ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Element Analysis ◽  
External Forces ◽  
Force Equilibrium

Numerous works have been done on modeling compliant modules or joints, and the closed-form models of many widely-used compliant modules have been developed. However, the modeling of complex compliant mechanisms with considering external forces is still a challenging work. This paper introduces a constraint-force-based method to model compliant mechanisms. A compliant mechanism can be regarded as the combination of rigid stages and compliant modules. If a compliant mechanism is at static equilibrium under the influence of a series of external forces, all the rigid stages are also at static equilibrium. The rigid stages are restricted by the constraint forces of the compliant modules and the exerted external forces. This paper defines the constraint forces of the compliant modules to be variable constraint forces since the constraint forces vary with the deformation of the compliant modules, and defines the external forces as constant constraint forces due to the fact that the external forces are specific forces exerted which do not change with the deformation of the compliant mechanism. Therefore, the force equilibrium equations for all rigid stages in a compliant mechanism can be obtained based on the variable constraint forces and the constant constraint forces. Moreover, the model of the compliant mechanism can also be derived through solving all the force equilibrium equations. The constraint-force-based modeling method is finally detailed demonstrated via examples, and validated by the finite element analysis. Using this proposed modeling method, a complex compliant mechanism can be modelled with a particular emphasis on considering the position spaces of the associated compliant modules.

Stiffness Estimation and Experiments for the Exechon Parallel Self-Reconfiguring Fixture Mechanism

2012 ◽  
Author(s):  
Xiong Li ◽  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Screw Theory ◽  
Virtual Work ◽  
Element Analysis ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Successful Series ◽  
Stiffness Model ◽  
Stiffness Map ◽  
Fixture System ◽  
Typical Configuration

The Exechon X150, a new smaller member of a successful series of parallel kinematic machines, has been recently developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. This paper is the first to address the stiffness analysis of the parallel mechanism on which the design is based. The stiffness modeling method uses reciprocal screw theory as well as the virtual work principle, resulting in a simpler formulation and more convenient than ones obtained with traditional stiffness-modeling methods. Based on this model, the stiffness map within the workspace is obtained. The stiffness of the mechanism at a typical configuration is carried out. The complete finite element analysis and simulation used to verify the effectiveness of the stiffness model. Using geometric spatial decomposition, numerical examples of the mechanism at three typical configurations are presented.

A Method to Evaluate and Calculate the Mobility of a General Compliant Parallel Manipulator

2004 ◽  
Author(s):  
Jingjun Yu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Kinematic Characteristic ◽  
Parallel Kinematic Machine ◽  
Compliance Matrix ◽  
Multiple Degrees Of Freedom ◽  
Parallel Kinematic

A compliant parallel manipulator (CPM), is a kind of compliant mechanism characterizes a complicate topological structure and multiple degrees of freedom. As one of the kinematic characteristics of a CPM, the mobility of a CPM become complicate compared to its rigid-counterpart. In order to describe such a complicate kinematic characteristic of a CPM, “primary mobility of a compliant parallel manipulator” concept is proposed. By means of the screw theory, a method of quantifying the primary mobility of the CPM is investigated under the ground that the compliance matrix of the manipulator should be calculated primarily. By using this method, the primary mobility of two typical compliant parallel manipulators, one is a planar 3-RRR CPM and the other a spatial 3-RRPR CPM, is addressed respectively. This proposed method is also instructive for analyzing the instantaneous mobility of a general degenerate-DOF parallel manipulator or a Parallel Kinematic Machine (PKM).

Tire Bead Overheating in Urban Buses and Trucks Using Drum Brake Systems

1998 ◽  
Vol 26 (1) ◽  
pp. 51-62
Author(s):  
A. L. A. Costa ◽  
M. Natalini ◽  
M. F. Inglese ◽  
O. A. M. Xavier
Keyword(s):  
Heat Transfer ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Thermal Energy ◽  
Structural Integrity ◽  
Experimental Temperature ◽  
Temperature Profiles ◽  
Element Analysis ◽  
Drum Brake ◽  
Fea Model

Abstract Because the structural integrity of brake systems and tires can be related to the temperature, this work proposes a transient heat transfer finite element analysis (FEA) model to study the overheating in drum brake systems used in trucks and urban buses. To understand the mechanics of overheating, some constructive variants have been modeled regarding the assemblage: brake, rims, and tires. The model simultaneously studies the thermal energy generated by brakes and tires and how the heat is transferred and dissipated by conduction, convection, and radiation. The simulated FEA data and the experimental temperature profiles measured with thermocouples have been compared giving good correlation.

scholarly journals A detailed study on design, fabrication, analysis, and testing of the anti-roll bar system for formula student cars

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Sachin Sunil Kelkar ◽  
Puneet Gautam ◽  
Shubham Sahai ◽  
Prajwal Sanjay Agrawal ◽  
R. Manoharan
Keyword(s):  
Material Selection ◽  
Analytical Calculation ◽  
Element Analysis ◽  
Static Testing ◽  
Shaft Diameter ◽  
Manufacturing Accuracy ◽  
Suspension Geometry ◽  
Aluminum 7075 ◽  
The One ◽  
Error Percentage

AbstractThis study explains a coherent flow for designing, manufacturing, analyzing, and testing a tunable anti-roll bar system for a formula student racecar. The design process starts with the analytical calculation for roll stiffness using constraining parameters such as CG (Center of Gravity) height, total mass, and weight distribution in conjunction with suspension geometry. Then, the material selection for the design i.e. Aluminum 7075 T6 is made based on parameters such as density and modulus of rigidity. A MATLAB program is used to iterate deflection vs load for different stiffness and shaft diameter values. This is then checked with kinematic deflection values in Solidworks geometry. To validate with the material deflection, finite element analysis is performed on ANSYS workbench. Manufacturing accuracy for the job is checked using both static analysis in lab settings and using sensors on vehicles during on-track testing. The error percentage is found to be 4% between the target stiffness and the one obtained from static testing. Parameters such as moment arm length, shaft diameter and length, and deflection were determined and validated. This paper shows the importance of an anti-roll bar device to tune the roll stiffness of the car without interfering with the ride stiffness.

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