A calibration method for overconstrained spatial translational parallel manipulators

Fengchun Li, Qiang Zeng, Kornel Ehmann, Jian Cao, Tiemin Li

Research output: Contribution to journalArticle

Abstract

A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

Original languageEnglish (US)
Pages (from-to)241-254
Number of pages14
JournalRobotics and Computer-Integrated Manufacturing
Volume57
DOIs
StatePublished - Jun 1 2019

Fingerprint

Parallel Manipulator
Kinematic Model
Manipulators
Calibration
Robots
Kinematics
End effectors
Parallel Robot
Robot
Integrated Model
Pyramid
Parallel Mechanism
Newton-Raphson
Methodology
Structural Parameters
Energy Method
Least Square Method
Ball
Verify
Iteration

Keywords

  • Calibration
  • Force method
  • Kinematic model
  • Overconstrained parallel mechanism

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Mathematics(all)
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

Cite this

@article{237b3866ce4742b699820d055b367de2,
title = "A calibration method for overconstrained spatial translational parallel manipulators",
abstract = "A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90{\%} are achievable.",
keywords = "Calibration, Force method, Kinematic model, Overconstrained parallel mechanism",
author = "Fengchun Li and Qiang Zeng and Kornel Ehmann and Jian Cao and Tiemin Li",
year = "2019",
month = "6",
day = "1",
doi = "10.1016/j.rcim.2018.12.002",
language = "English (US)",
volume = "57",
pages = "241--254",
journal = "Robotics and Computer-Integrated Manufacturing",
issn = "0736-5845",
publisher = "Elsevier Limited",

}

A calibration method for overconstrained spatial translational parallel manipulators. / Li, Fengchun; Zeng, Qiang; Ehmann, Kornel; Cao, Jian; Li, Tiemin.

In: Robotics and Computer-Integrated Manufacturing, Vol. 57, 01.06.2019, p. 241-254.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A calibration method for overconstrained spatial translational parallel manipulators

AU - Li, Fengchun

AU - Zeng, Qiang

AU - Ehmann, Kornel

AU - Cao, Jian

AU - Li, Tiemin

PY - 2019/6/1

Y1 - 2019/6/1

N2 - A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

AB - A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

KW - Calibration

KW - Force method

KW - Kinematic model

KW - Overconstrained parallel mechanism

UR - http://www.scopus.com/inward/record.url?scp=85058542485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058542485&partnerID=8YFLogxK

U2 - 10.1016/j.rcim.2018.12.002

DO - 10.1016/j.rcim.2018.12.002

M3 - Article

VL - 57

SP - 241

EP - 254

JO - Robotics and Computer-Integrated Manufacturing

JF - Robotics and Computer-Integrated Manufacturing

SN - 0736-5845

ER -