Next Article in Journal / Special Issue
Additive Manufacturing as an Essential Element in the Teaching of Robotics
Previous Article in Journal
Development of a Practical Tool for Designing Multi-Robot Systems in Pick-and-Place Applications
Previous Article in Special Issue
Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles
Article Menu

Export Article

Open AccessFeature PaperArticle

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Workgroup on System Technologies and Engineering Design Methodology, Hamburg University of Technology, 21073 Hamburg, Germany
Robotics 2019, 8(3), 72; https://doi.org/10.3390/robotics8030072
Received: 7 June 2019 / Revised: 9 August 2019 / Accepted: 13 August 2019 / Published: 16 August 2019
(This article belongs to the Special Issue Kinematics and Robot Design II, KaRD2019)
PDF [7503 KB, uploaded 16 August 2019]
  |     |  

Abstract

In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.
Keywords: direct kinematics problem; parallel robots; linear actuators’ orientations; assembly modes; general planar 3-RPR parallel mechanism; inertial measurement units; Cramér-Rao lower bound; static and dynamic experiments direct kinematics problem; parallel robots; linear actuators’ orientations; assembly modes; general planar 3-RPR parallel mechanism; inertial measurement units; Cramér-Rao lower bound; static and dynamic experiments
Figures

Graphical abstract

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Supplementary materials

SciFeed

Share & Cite This Article

MDPI and ACS Style

Schulz, S. Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations. Robotics 2019, 8, 72.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Robotics EISSN 2218-6581 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top