Sensitivity Analysis of the Orthoglide: A Three-DOF Translational Parallel Kinematic Machine

In this paper, two complementary methods are introduced to analyze the sensitivity of a three-degree-of-freedom (3-DOF) translational parallel kinematic machine (PKM) with orthogonal linear joints: the Orthoglide. Although these methods are applied to a particular PKM, they can be readily applied to 3-DOF Delta-Linear PKM such as ones with their linear joints parallel instead of orthogonal. On the one hand, a linkage kinematic analysis method is proposed to have a rough idea of the influence of the length variations of the manipulator on the location of its end-effector. On the other hand, a differential vector method is used to study the influence of the length and angular variations in the parts of the manipulator on the position and orientation of its end-effector. Besides, this method takes into account the variations in the parallelograms. It turns out that variations in the design parameters of the same type from one leg to another have the same effect on the position of the end-effector. Moreover, the sensitivity of its pose to geometric variations is a minimum in the kinematic isotropic configuration of the manipulator. On the contrary, this sensitivity approaches its maximum close to the kinematic singular configurations of the manipulator.

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Sensitivity Analysis of the Orthoglide, a 3-DOF Translational Parallel Kinematic Machine

Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2004-57379 ◽

2004 ◽

Cited By ~ 3

Author(s):

Ste´phane Caro ◽

Philippe Wenger ◽

Fouad Bennis ◽

Damien Chablat

Keyword(s):

Sensitivity Analysis ◽

Kinematic Analysis ◽

Design Parameters ◽

Analysis Method ◽

Parallel Kinematic Machine ◽

Vector Method ◽

End Effector ◽

Singular Configurations ◽

Parallel Kinematic ◽

Position And Orientation

This paper presents a sensitivity analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. Two complementary methods are used to analyze its sensitivity to its dimensional and angular variations. First, a linkage kinematic analysis method is used to have a rough idea of the influence of the dimensional variations on the location of the end-effector, and shows that the variations in design parameters of the same type from one leg to another one have the same influence on the end-effector. However, this method does not allow the designer to know the influence of the variations in the parallelograms. Thus, a differential vector method is used to study the influence of the dimensional and angular variations in the parts of the manipulator, and particularly the variations in the parallelograms, on the position and orientation of the end-effector. It turns out that the isotropic kinematic configuration of the manipulator is the least sensitive one to its geometrical variations, contrary to the closest configurations to its kinematic singular configurations, which are the most sensitive to geometrical variations.

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Constraint and Singularity Analysis of the Exechon Tripod

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-71184 ◽

2012 ◽

Cited By ~ 8

Author(s):

Dimiter Zlatanov ◽

Matteo Zoppi ◽

Rezia Molfino

Keyword(s):

Machine Tool ◽

System Approach ◽

Parallel Mechanism ◽

Singularity Analysis ◽

Geometric Interpretation ◽

End Effector ◽

Singular Configurations ◽

Parallel Kinematic ◽

Three Degree Of Freedom ◽

Fixture System

The paper discusses mobility and singularities of the Exechon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exechon designs are used by a number of machine-tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.

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Error estimation and sensitivity analysis of the 3-UPU translational parallel robot due to design parameter uncertainties

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406218793673 ◽

2018 ◽

Vol 233 (8) ◽

pp. 2713-2727 ◽

Cited By ~ 4

Author(s):

S El Hraiech ◽

AH Chebbi ◽

Z Affi ◽

L Romdhane

Keyword(s):

Sensitivity Analysis ◽

Vertical Axis ◽

Parallel Robot ◽

Design Parameters ◽

Analysis Method ◽

Parameter Uncertainties ◽

End Effector ◽

Interval Analysis Method ◽

Influential Parameters ◽

Kinematic Errors

This work deals with the estimation and the sensitivity analysis of the 3-UPU parallel robot error. Based on the Newton–Euler formalism, the robot dynamic model is given in a closed form. This model is validated by the software ADAMS. Using the interval analysis method, a new algorithm is proposed, which estimates the errors in the motion of the end-effector and the errors in the actuator forces as a function of the design parameters uncertainties. The obtained results show that the kinematic errors are minimal at the workspace center. Moreover, these errors increase as the platform moves along the vertical axis. It is also shown that kinematic errors in the actuator joints are the most influential parameters on the manipulator accuracy. Therefore, using actuators with a higher accuracy can highly reduce the errors in motion of the platform.

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PATH PLACEMENT OPTIMIZATION OF MANIPULATORS BASED ON ENERGY CONSUMPTION: APPLICATION TO THE ORTHOGLIDE 3-AXIS

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-2009-0035 ◽

2009 ◽

Vol 33 (3) ◽

pp. 523-541 ◽

Cited By ~ 4

Author(s):

Raza Ur-Rehman ◽

Stéphane Caro ◽

Damien Chablat ◽

Philippe Wenger

Keyword(s):

Energy Consumption ◽

Optimal Path ◽

Electric Energy ◽

Optimal Location ◽

Degree Of Freedom ◽

Parallel Kinematic Machine ◽

Dynamic Constraints ◽

Placement Optimization ◽

Parallel Kinematic ◽

Three Degree Of Freedom

This paper deals with the optimal path placement for a manipulator based on energy consumption. It proposes a methodology to determine the optimal location of a given test path within the workspace of a manipulator with minimal electric energy used by the actuators while taking into account the geometric, kinematic and dynamic constraints. The proposed methodology is applied to the Orthoglide 3-axis, a three-degree-of-freedom translational parallel kinematic machine (PKM), as an illustrative example.

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A New 4-DOF Fully Parallel Robot With Decoupled Rotation for Five-Axis Micromachining Applications

Journal of Mechanisms and Robotics ◽

10.1115/1.4042849 ◽

2019 ◽

Vol 11 (3) ◽

Cited By ~ 1

Author(s):

Oleksandr Stepanenko ◽

Ilian A. Bonev ◽

Dimiter Zlatanov

Keyword(s):

Degrees Of Freedom ◽

Mechanical Design ◽

Parallel Robot ◽

Parallel Kinematic Machine ◽

Constant Length ◽

End Effector ◽

Kinematic Models ◽

Parallel Kinematic ◽

Linear Actuators ◽

Five Axis

We present a novel 4-DOF (degrees of freedom) parallel robot designed for five-axis micromachining applications. Two of its five telescoping legs operate simultaneously, thus acting as an extensible parallelogram linkage, and in conjunction with two other legs control the position of the tooltip. The fifth leg controls the tilt of the end-effector (a spindle), while a turntable fixed at the base of the robot controls the swivel of the workpiece. The robot is capable of tilting its end-effector up to 90 deg, for any tooltip position. In this paper, we study the mobility of the new parallel kinematic machine (PKM), describe its inverse and direct kinematic models, then study its singularities, and analyze its workspace. Finally, we propose a potential mechanical design for this PKM utilizing telescopic actuators as well as the procedure for optimizing it. In addition, we discuss the possibility of using constant-length legs and base-mounted linear actuators in order to increase the volume of the workspace.

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Error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405418782283 ◽

2018 ◽

Vol 233 (6) ◽

pp. 1637-1652 ◽

Cited By ~ 6

Author(s):

Xuan Luo ◽

Fugui Xie ◽

Xin-Jun Liu ◽

Jie Li

Keyword(s):

Sensitivity Analysis ◽

Machine Tool ◽

Jacobian Matrix ◽

Error Modeling ◽

Degree Of Freedom ◽

Geometric Errors ◽

Parallel Kinematic Machine ◽

Parallel Kinematic ◽

Position And Orientation ◽

Five Axis

5-Degree-of-freedom parallel kinematic machine tools are always attractive in manufacturing industry due to the ability of five-axis machining with high stiffness/mass ratio and flexibility. In this article, error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool are discussed for its accuracy issues. An error modeling method based on screw theory is applied to each limb, and then the error model of the parallel kinematic machine tool is established and the error mapping Jacobian matrix of 53 geometric errors is derived. Considering that geometric errors exert both impacts on value and direction of the end-effector’s pose error, a set of sensitivity indices and an easy routine for sensitivity analysis are proposed according to the error mapping Jacobian matrix. On this basis, 10 vital errors and 10 trivial errors are identified over the prescribed workspace. To validate the effects of sensitivity analysis, several numerical simulations of accuracy design are conducted, and three-dimensional model assemblies with relevant geometric errors are established as well. The simulations exhibit maximal −0.10% and 0.34% improvements of the position and orientation errors, respectively, after modifying 10 trivial errors, while minimal 65.56% and 55.17% improvements of the position and orientation errors, respectively, after modifying 10 vital errors. Besides the assembly reveals an output pose error of (0.0134 mm, 0.0020 rad) with only trivial errors, while (2.0338 mm, 0.0048 rad) with only vital errors. In consequence, both results of simulations and assemblies validate the correctness of the sensitivity analysis. Moreover, this procedure can be extended to any other parallel kinematic mechanisms easily.

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Generalized Singularity Analysis of Snake-Like Robot

Applied Sciences ◽

10.3390/app8101873 ◽

2018 ◽

Vol 8 (10) ◽

pp. 1873 ◽

Cited By ~ 2

Author(s):

Shunsuke Nansai ◽

Masami Iwase ◽

Hiroshi Itoh

Keyword(s):

Singularity Analysis ◽

Common Point ◽

Analysis Method ◽

Link Length ◽

New Model ◽

Singular Configurations ◽

Singular Configuration ◽

The One

The purpose of this paper is to elucidate a generalized singularity analysis of a snake-like robot. The generalized analysis is denoted as analysis of singularity of a model which defines all designable parameters such as the link length and/or the position of the passive wheel as arbitrary variables. The denotation is a key point for a novelty of this study. This paper addresses the above new model denotation, while previous studies have defined the designable parameters as unique one. This difference makes the singularity analysis difficult substantively. To overcome this issue, an analysis method using redundancy of the snake-like robot is proposed. The proposed method contributes to simplify singularity analysis concerned with the designable parameters. The singular configurations of both the model including side-slipping and the one with non side-slipping are analyzed. As the results of the analysis, we show two contributions. The first contribution is that a singular configuration depends on designable parameters such as link length as well as state values such as relative angles. The second contribution is that the singular configuration is characterized by the axials of the passive wheels of all non side-slipping link. This paper proves that the singular configuration is identified as following two conditions even if the designable parameters are chosen as different variables and the model includes side-slipping link. One is that the axials of passive wheels of all non side-slipping links intersect at a common point. Another one is that axials of passive wheels of all non side-slipping links are parallel.

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Design optimization of the linkage dimension for a hybrid-type parallel kinematic machine tool

Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics ◽

10.1243/14644190260070385 ◽

2002 ◽

Vol 216 (2) ◽

pp. 143-156 ◽

Cited By ~ 2

Author(s):

T-H Chang ◽

S-L Chen ◽

C-A Kang ◽

I Inasaki

Keyword(s):

Machine Tool ◽

Machine Tools ◽

Inverse Kinematics ◽

Design Parameters ◽

Parallel Kinematic Machine ◽

Design Procedures ◽

Research Fields ◽

Hybrid Mechanism ◽

Parallel Kinematic ◽

Accumulated Error

The parallel kinematic machine tool has many advantages including excellent loading capacity, high structural stiffness and small accumulated error of linkage. It has become one of the most important research fields for machine tools. In the present research, a principle for the optimization of the dimensional design parameters of a parallel kinematic machine tool is proposed. A five-degree-of-freedom (5DOF) parallel kinematic machine tool with a TRR-XY hybrid mechanism is chosen for investigating the design procedures and the optimization results. The inverse kinematics of the hybrid mechanism is first investigated. Then, the inverse solution is used to analyse and create the workspaces of the machine tool. The design parameters of the mechanical components are further optimized for constructing the maximum workspace.

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Hybrid-model-based stiffness analysis of a three-revolute-prismatic-spherical parallel kinematic machine

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405416634257 ◽

2016 ◽

Vol 231 (14) ◽

pp. 2561-2576 ◽

Cited By ~ 4

Author(s):

Jun Zhang ◽

Yan Q Zhao ◽

Hai W Luo

Keyword(s):

High Speed ◽

Experimental Tests ◽

Design Parameters ◽

Parallel Kinematic Machine ◽

Modeling Methodology ◽

Parallel Kinematic ◽

Stiffness Characteristics ◽

And Performance ◽

High Dynamics ◽

Spring Constants

A three-revolute-prismatic-spherical parallel kinematic machine is proposed as an alternative solution for high-speed machining tool due to its high rigidity and high dynamics. Considering the parallel kinematic machine module as a typical compliant parallel mechanism, whose three limb assemblages have bending, extending and torsional deflections, this article proposes a hybrid modeling methodology to establish an analytical stiffness model for the three-revolute-prismatic-spherical device. The developed analytical model is further used to evaluate the stiffness mapping of the three-revolute-prismatic-spherical module over a given work plane which is then validated by experimental tests. The simulations and experiments indicate that the present hybrid methodology can predict the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness in a quick and accurate manner. The solution for eigenvalue problem of the stiffness matrix leads to the stiffness characteristics of the parallel module including eigenstiffnesses and the corresponding eigenscrews as well as the equivalent screw spring constants. Based on the eigenscrew decomposition, the parallel kinematic machine is physically interpreted as a rigid platform suspending by six screw springs. The minimum, maximum and average of the screw spring constants are chosen as indices to assess the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness performance. The distributions of the proposed indices throughout the workspace reveal a strong dependency on the mechanism’s configurations. At the final stage, the effects of some design parameters on system stiffness characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement of the parallel kinematic machine.

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