Error Space Estimation of Three Degrees of Freedom Planar Parallel Mechanisms

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Jianzhong Ding ◽  
Shengnan Lyu ◽  
Ting Da ◽  
Chunjie Wang ◽  
Gregory S. Chirikjian
Keyword(s):  
Degrees Of Freedom ◽  
Geometric Error ◽  
Closed Form Expression ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Interval Analysis Method ◽  
Minimum Volume Ellipsoid ◽  
Error Space ◽  
Joint Clearances ◽  
Constraint Modeling

This paper develops a geometric method to estimate the error space of 3-DOF planar mechanisms with the Minimum Volume Ellipsoid Enclosing (MVEE) approach. Both the joint clearances and actuator errors are considered in this method. Three typical planar parallel mechanisms are used to demonstrate. Error spaces of their serial limbs are analyzed. Thereafter, limb-error-space-constrained mobility of the manipulator, namely, the manipulator error space is analyzed. The MVEE method has been applied to simplify the constraint modeling. A closed-form expression for the manipulator error space is derived. The volume of the manipulator error space is numerically estimated. The approach in this paper is to develop a geometric error analysis method of parallel mechanisms with clear algebraic expressions. Moreover, no forward kinematics computations have been performed in the proposed method, in contrast to the widely used interval analysis method. Although the estimated error space is larger than the actual one, because the enclosing ellipses enlarge the regions of limb error space, the method has an attractive advantage of high computational efficiency.

Conservative Error Space Estimation of 3-DoF Planar Parallel Mechanisms

2018 ◽  
Author(s):  
Jianzhong Ding ◽  
Shengnan Lu ◽  
Ting Da ◽  
Chunjie Wang ◽  
Gregory S. Chirikjian
Keyword(s):  
Geometric Error ◽  
Closed Form Expression ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Planar Mechanisms ◽  
Interval Analysis Method ◽  
Minimum Volume Ellipsoid ◽  
Error Space ◽  
Constraint Modeling ◽  
Estimated Error

This article develops a geometric method to estimate the error space of 3-DoF planar mechanisms with the Minimum Volume Ellipsoid Enclosing (MVEE) approach. Both the joint clearance and input uncertainty are considered in this method. Three typical planar parallel mechanisms are used to demonstrate. Error spaces of their serial limbs are analyzed, respectively. Thereafter, limb-error-space-constrained mobility of manipulator, namely, the manipulator error space is analyzed. MVEE method has been applied to simplify the constraint modeling. A closed-form expression for the manipulator error space is derived. The volume of the manipulator error space is numerically estimated. The study approached in this paper develops a geometric error analysis method of parallel mechanisms with clear algebraic expressions. Moreover, far fewer forward kinematics computations have been performed in the proposed method than in the widely used interval analysis method. Although the estimated error space is larger than that in practice, due to the enclosing ellipses enlarge the regions of limb error space, the method has attractive advantage of high computational efficiency.

Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Qinchuan Li ◽  
Xinxue Chai ◽  
Ji'nan Xiang
Keyword(s):  
Basic Property ◽  
Geometric Algebra ◽  
Degrees Of Freedom ◽  
Linear Equations ◽  
Closed Form Expression ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Mobility Analysis ◽  
Form Expression ◽  
General Method

Mobility is a basic property of a mechanism. The aim of mobility analysis is to determine the number of degrees-of-freedom (DOF) and the motion pattern of a mechanism. The existing methods for mobility analysis have some drawbacks when being applied to limited-DOF parallel mechanisms (PMs). Particularly, it is difficult to obtain a symbolic or closed-form expression of mobility and its geometric interpretations are not always straightforward. This paper presents a general method for mobility analysis of limited-DOF PMs in the framework of geometric algebra. The motion space and constraint space of each limb are expressed using geometric algebra. Then the mobility of the PM can be calculated based on the orthogonal complement relationship between the motion space and the constraint space. The detailed mobility analyses of a 3-RPS PM and a 3-RPC PM are presented. It is shown that this method can obtain a symbolic expression of mobility with straightforward geometric interpretations and is applicable to limited-DOF PMs with or without redundant constraints. Without solving complicated symbolic linear equations, this method also has computational advantages.

A novel accuracy model for the intrinsic kinematic property of a prismatic pair

2018 ◽  
Vol 232 (15) ◽  
pp. 2697-2710
Author(s):  
Yu Wu ◽  
Zhi Wang ◽  
Huimin Dong ◽  
Delun Wang
Keyword(s):  
Degrees Of Freedom ◽  
Geometric Error ◽  
Kinematic Characteristic ◽  
Equilibrium Equations ◽  
Tool Manufacture ◽  
Error Surface ◽  
Kinematic Property ◽  
Error Space ◽  
Set Up ◽  
Straightness Error

A novel accuracy model is proposed to analyze the intrinsic kinematic property of the prismatic pair. The geometric error of guide rails, the elastic constrained structure of moving joints, and fixed joints are considered synthetically. The geometric error is measured by the 5D laser interferometer system with slide blocks. The elastic moving joints are equivalent to the springs, while the fixed joints to contact layers. The equilibrium equations are then set up and the analytical solution for five degrees-of-freedom errors of the moving table is revealed. The global invariant errors, including the straightness error space and the spherical image error surface, are proposed to describe the global kinematic characteristic of the moving table. Along with the comparison between the measured and theoretical indicators, the verification experiment to prove the availability of the model is carried out. As the movement of the table can be forecast precisely and evaluated objectively, the new methodology provides a theoretical basis for machine tool manufacture.

Experimental Validation of Jacobian-Based Stiffness Analysis Method for Parallel Manipulators With Nonredundant Legs

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Antonius G. L. Hoevenaars ◽  
Clément Gosselin ◽  
Patrice Lambert ◽  
Just L. Herder
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Stiffness Analysis ◽  
Levels Of Detail ◽  
Structural Compliance

A complete stiffness analysis of a parallel manipulator considers the structural compliance of all elements, both in designed degrees-of-freedom (DoFs) and constrained DoFs, and also includes the effect of preloading. This paper presents the experimental validation of a Jacobian-based stiffness analysis method for parallel manipulators with nonredundant legs, which considers all those aspects, and which can be applied to limited-DoF parallel manipulators. The experimental validation was performed by comparing differential wrench measurements with predictions based on stiffness analyses with increasing levels of detail. For this purpose, two passive parallel mechanisms were designed, namely, a planar 3DoF mechanism and a spatial 1DoF mechanism. For these mechanisms, it was shown that a stiffness analysis becomes more accurate if preloading and structural compliance are considered.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

Structural Modification Simulation: Sensitivity Analysis and the Reanalysis of Modified Structure

1991 ◽  
Author(s):  
Debao Li ◽  
Fangze Li ◽  
Peiming Xu
Keyword(s):  
Sensitivity Analysis ◽  
Transfer Function ◽  
Coordinate Transformation ◽  
Degrees Of Freedom ◽  
Structural Modification ◽  
Function Analysis ◽  
Dump Truck ◽  
Analysis Method ◽  
Transfer Function Analysis ◽  
Dynamic Modification

Abstract This paper deals with the dynamic modification simulation of the structure. The expressions of sensitivity analysis of the system with non-proportional damping and proportional damping are derived at first. As for the reanalysis of modified structure, here we deal with the system to which the modification do not cause any change of the degrees of freedom. Transfer function analysis method and the method of twice coordinate transformation are expounded. As a successful example, the modification simulation of the frame of a dump truck is explained.

A Parallely Actuated Work Support Module for Reconfigurable Machining Systems

1998 ◽  
Author(s):  
Venkat Gopalakrishnan ◽  
Sridhar Kota
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Performance Criteria ◽  
Machining Accuracy ◽  
Parallel Mechanisms ◽  
Element Analysis ◽  
Work Support ◽  
Reconfigurable Machining

Abstract In order to respond quickly to changes in market demands and the resulting product design changes, machine tool manufacturers must reduce the machine tool design lead time and machine set-up time. Reconfigurable Machine Tools (RMTs), assembled from machine modules such as spindles, slides and worktables are designed to be easily reconfigured to accommodate new machining requirements. The essential characteristics of RMTs are modularity, flexibility, convertibility and cost effectiveness. The goal of Reconfigurable Machining Systems (RMSs), composed of RMTs and other types of machines, is to provide exactly the capacity and functionality, exactly when needed. The scope of RMSs design includes mechanical hardware, control systems, process planning and tooling. One of the key challenges in the mechanical design of reconfigurable machine tools is to achieve the desired machining accuracy in all intended machine configurations. To meet this challenge we propose (a) to distribute the total number of degrees of freedom between the work-support and the tool and (b) employ parallely-actuated mechanisms for stiffness and ease of reconfigurability. In this paper we present a novel parallely-actuated work-support module as a part of an RMT. Following a brief summary of a few parallel mechanisms used in machine tool applications, this paper presents a three-degree-of-freedom work-support module designed to meet the machining requirements of specific features on a family of automotive cylinder heads. Inverse kinematics, dynamic and finite element analysis are performed to verify the performance criteria such as workspace envelope and rigidity. A prototype of the proposed module is also presented.

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