What is the effect of the error bound analysis on the accuracy of a planar parallel manipul?

Kim et al. [2] used a forward error bound analysis to find the error bound of the end-effector of a Stewart platform when the error bounds of the joints are given, and an inverse error bound analysis to determine those of the joints for the given error bound of the end-effector.

What is the sensitivity of the 3-RPR manipulator under study?

For that matter, let N f be a normalizing factor:N f = (R1 +R2)/2 (1)andrm = Rm/N f , m = 1,2 (2)Therefore,r1 + r2 = 2 (3)From Eqs.(2) and (3), the authors can notice that:r1 ∈ [0,2] , r2 ∈ [0,2] (4)As the former two-dimensional infinite space corresponding to geometric parameters R1 and R2 is reduced to a one-dimensional finite space defined with Eq.(3), the workspace analysis of the 3-RPR manipulator under study turns out to be easier.

What is the kinematic Jacobian matrix of the manipulator?

J is the kinematic Jacobian matrix of the manipulator whereas Ja, Jα, Jc and Jβ are named sensitivity Jacobian matrices of the pose of the MP to variations in ai, αi, ci and βi, respectively.

How is the pose of the manipulator determined?

The pose of the manipulator MP, i.e., its position and its orientation, is determined by means of the Cartesian coordinates vector p = [px, py]

What are the sensitivity Jacobian matrices of the manipulator?

The pose errors of the manipulator MP depend on variations in the geometric parameters as well as on the manipulator configuration.

What is the sensitivity of the position of the manipulator to variations in its geometric parameters?

from Eq.(30b), an aggregate sensitivity index νp of the position of the MP of the manipulator to variations in its geometric parameters and prismatic actuated joints can be defined as follows:νp = ‖Jsp‖2nv (32)For any given manipulator configuration, the lower νφ, the lower the overall sensitivity of the orientation of its MP to variations in the geometric parameters.

Open AccessJournal Article10.1007/S11012-010-9390-0

Comparison of 3-RPR planar parallel manipulators with regard to their kinetostatic performance and sensitivity to geometric uncertainties

Nicolas Binaud, +2 more

- 01 Feb 2011

- Meccanica

- Vol. 46, Iss: 1, pp 75-88

TL;DR: In this paper, the sensitivity analysis of 3-RPRP planar parallel manipulators with respect to dexterity, workspace size, and sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically.

Abstract: This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators First, the manipulators under study as well as their degeneracy conditions are presented Then, an optimization problem is formulated in order to obtain their maximal regular dexterous workspace Moreover, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically Two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position Then, we compare two non-degenerate and two degenerate 3-RPR planar parallel manipulators with regard to their dexterity, workspace size and sensitivity Finally, two actuating modes are compared with regard to their sensitivity

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Most frequently asked questions

1. What are the contributions mentioned in the paper "Comparison of 3-rpr planar parallel manipulators with regard to their dexterity and sensitivity to geometric uncertainties" ?

Binaud et al. this paper analyzed the sensitivity of 3-RPR planar parallel manipulators to geometric uncertainties.

2. What is the actuating mode of the first limb?

the eighth actuating mode corresponds to the 3-RPR PPM, also called RPR1-RPR2-RPR3 PPM, as the prismatic joints of its limbs are actuated.

3. What is the transmission angle of a 3-DOF PPM?

In the scope of this study, the RDW of the PPM is supposed to be a cylinder of φ-axis with good kinetostatic performance, i.e., the transmission angle ψ is smaller than 75◦ throughout the cylinder.

4. What is the first actuating mode of the RPR1-RPR2 PPM?

For instance, the first actuating mode corresponds to the 3- RPR PPM, also called RPR1-RPR2-RPR3 PPM in the scope of this paper, as the first revolute joints (located at points Ai) of its limbs are actuated.

Figure 2. The four 3-RPR manipulators under study with φ = 0 and p = [1,1.5]T : (a)-(b) non-degenerate manipulators, (c)-(d) degenerate manipulators

Figure 5. νφ isocontours of: (a) M1, (b) M2, (c) M3 and (d) M4

Table 1. Cartesian coordinates of instantaneous centres of rotation

Figure 11. (a) M1 νp and (b) M5 νp isocontours

Figure 12. Comparison of •—•: M1 and ⋆—⋆: M5

Figure 10. (a) M1 νφ and (b) M5 νφ isocontours

Citations

Journal Article•10.1016/J.EUROMECHSOL.2012.05.009

Clearance and manufacturing errors' effects on the accuracy of the 3-RCC Spherical Parallel Manipulator

Abdelbadiâ Chaker, +4 more

- 01 Jan 2013

- European Journal of Mechanics A-solids

TL;DR: In this paper, the authors deal with the analysis of a spherical parallel manipulator (3RCC) to determine the error on the pose of the end effector as a function of the manufacturing errors of the different links and the presence of a clearance in the joints.

...read moreread less

Journal Article•10.1139/TCSME-2011-0028

Geometric analysis of the kinematic sensitivity of planar parallel mechanisms

Mohammad Hossein Saadatzi, +4 more

- 01 Dec 2011

- Transactions of The Canadian Society for...

TL;DR: In this article, a robust geometric approach for computing the kinematic sensitivity index for the case of planar parallel mechanisms is presented, and the physical meaning of kinematics is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples.

...read moreread less

Journal Article•10.1007/S40997-016-0019-3

Dynamic Performance Evaluation of Serial and Parallel RPR Manipulators with Flexible Intermediate Links

Saeed Ebrahimi, +1 more

- 28 Jun 2016

- Iranian Journal of Science and Technolog...

TL;DR: It is concluded that, in addition to the specific structure of the manipulator, the accuracy generally depends on the operation conditions, and contest the general assertion which claims that parallel manipulators have more accuracy and stiffness than serial counterparts.

...read moreread less

Journal Article•10.1017/S0263574716000291

A comparative study of elastic motions in trajectory tracking of flexible RPR planar manipulators moving with high speed

Amirhossein Eshaghiyeh Firoozabadi, +2 more

- 01 Jul 2017

- Robotica

TL;DR: In some cases, adding each extra RPR chain in the n-RPR planar manipulators with flexible intermediate links reduces the stiffness and accuracy due to the inertial forces of the flexible links, which is opposite to what would be expected.

...read moreread less

Proceedings Article•10.1109/ICROM.2017.8466159

Kinematic Sensitivity Evaluation of Revolute and Prismatic 3-DOF Delta Robots

Behzad Mehrafrooz, +2 more

- 01 Oct 2017

TL;DR: The results of this paper revealed that kinematic sensitivity indices can be employed in the design step of the robot to reach an optimal kinematics sensitivity in the workspace.

...read moreread less

...

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References

•Book

Kinematic geometry of mechanisms

Kenneth Henderson Hunt

- 01 Jan 1978

TL;DR: The components of mechanism freedom and structure in mechanism elementary planar and spatial displacements planar algebraic curves infinitesimal planar kinematics planar displacements through three and more locations the four-bar linkage - coupler curves the geometrical capability of planar mechanisms three-dimensional geometry and spatial mechanism some spatial mechanisms line geometry, and spatial mechanisms screw systems screw systems applied to spatial mechanisms body guidance in three dimensions manipulator-arms and other linkageconnections.

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Journal Article•10.1109/70.56660

Singularity analysis of closed-loop kinematic chains

Clément Gosselin, +1 more

- 01 Jun 1990

TL;DR: The different kinds of singularities encountered in closed-loop kinematics chains are analyzed and a general classification of these singularities in three main groups, based on the properties of the Jacobian matrices of the chain, is described.

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1.8K

Journal Article•10.1115/1.3258540

Structural Kinematics of In-Parallel-Actuated Robot-Arms

Kenneth H. Hunt

- 01 Dec 1983

- Journal of Mechanisms Transmissions and ...

909

Journal Article•10.1115/1.1543977

Design Optimization of a Cartesian Parallel Manipulator

Han Sung Kim, +1 more

- 01 Jan 2002

- Journal of Mechanical Design

TL;DR: The Cartesian Parallel Manipulator (CPM) as mentioned in this paper consists of a moving platform that is connected to a fixed base by three limbs and each limb is made up of one prismatic and three revolute joints and all joint axes are parallel to one another.

...read moreread less

241

Journal Article•10.1016/J.MECHMACHTHEORY.2005.05.004

Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms

Xin-Jun Liu, +2 more

- 01 Feb 2006

- Mechanism and Machine Theory

TL;DR: In this paper, a non-dimensional design space is established to investigate the singular loci and workspace shape of the 5R symmetrical parallel mechanisms, systematically, and the atlas of the maximal inscribed workspace (MIW) radius is presented.

...read moreread less

171

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Comparison of 3-RPR planar parallel manipulators with regard to their kinetostatic performance and sensitivity to geometric uncertainties

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions mentioned in the paper "Comparison of 3-rpr planar parallel manipulators with regard to their dexterity and sensitivity to geometric uncertainties" ?

2. What is the actuating mode of the first limb?

3. What is the transmission angle of a 3-DOF PPM?

4. What is the first actuating mode of the RPR1-RPR2 PPM?

5. What is the effect of the error bound analysis on the accuracy of a planar parallel manipul?

6. What is the sensitivity of the 3-RPR manipulator under study?

7. What is the kinematic Jacobian matrix of the manipulator?

8. How is the pose of the manipulator determined?

9. What are the sensitivity Jacobian matrices of the manipulator?

10. What is the sensitivity of the position of the manipulator to variations in its geometric parameters?

Figures

Citations

Clearance and manufacturing errors' effects on the accuracy of the 3-RCC Spherical Parallel Manipulator

Geometric analysis of the kinematic sensitivity of planar parallel mechanisms

Dynamic Performance Evaluation of Serial and Parallel RPR Manipulators with Flexible Intermediate Links

A comparative study of elastic motions in trajectory tracking of flexible RPR planar manipulators moving with high speed

Kinematic Sensitivity Evaluation of Revolute and Prismatic 3-DOF Delta Robots

References

Kinematic geometry of mechanisms

Singularity analysis of closed-loop kinematic chains

Structural Kinematics of In-Parallel-Actuated Robot-Arms

Design Optimization of a Cartesian Parallel Manipulator

Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms

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