Research Papers

Design and Kinematics Modeling of a Novel 3-DOF Monolithic Manipulator Featuring Improved Scott-Russell Mechanisms

[+] Author and Article Information
Yanding Qin

Tianjin Key Laboratory
of Intelligent Robotics
Nankai University,
Tianjin 300071, China
e-mail: qinyd@nankai.edu.cn

Bijan Shirinzadeh

Robotics and Mechatronics
Research Laboratory,
Department of Mechanical
and Aerospace Engineering,
Monash University,
Clayton VIC 3800, Australia
e-mail: bijan.shirinzadeh@monash.edu

Dawei Zhang

e-mail: medzhang@tju.edu.cn

Yanling Tian

e-mail: meytian@tju.edu.cn
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received October 2, 2012; final manuscript received June 16, 2013; published online August 21, 2013. Assoc. Editor: Feng Gao.

J. Mech. Des 135(10), 101004 (Aug 21, 2013) (9 pages) Paper No: MD-12-1485; doi: 10.1115/1.4024979 History: Received October 02, 2012; Revised June 16, 2013

This paper proposes the design of a novel 3-DOF monolithic manipulator. This manipulator is capable of performing planar manipulations with three kinematically coupled DOFs, i.e., the translations in the X and Y axes and the rotation about the Z axis. An improved Scott-Russell (ISR) mechanism is utilized to magnify the displacement of the piezoelectric actuator (PEA). Unlike the SR mechanism, a set of leaf parallelograms is incorporated into the drive point of the ISR mechanism as a prismatic joint. As a result, the linearity of motion and stability are improved. With circular flexure hinges being treated as revolute joints, the forward kinematics and inverse kinematics of the 3-DOF manipulator are analytically derived. Computational analyses are performed to validate the established kinematics models. Due to the unwanted compliance of the flexure hinges, the actual displacement amplification ratio of the ISR mechanism is smaller than its theoretical value. This is the main cause of the discrepancies between the analytical and computational results. The reachable workspace and the static/dynamic characteristics of the 3-DOF manipulator are also analyzed.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Kenton, B. J., and Leang, K. K., 2012, “Design and Control of a Three-Axis Serial-Kinematic High-Bandwidth Nanopositioner,” IEEE/ASME Trans. Mech., 17(2), pp. 356–369. [CrossRef]
Zubir, M. N. M., Shirinzadeh, B., and Tian, Y., 2009, “Development of a Novel Flexure-Based Microgripper for High Precision Micro-Object Manipulation,” Sens. Actuators, A, 150(2), pp. 257–266. [CrossRef]
Kuhnen, K., 2003, “Modelling, Identification and Compensation of Complex Hysteretic Nonlinearities—A Modified Prandtl-Ishlinskii Approach,” Eur. J. Control, 9(4), pp. 407–418. [CrossRef]
Qin, Y., Tian, Y., Zhang, D., Shirinzadeh, B., and Fatikow, S., 2013, “A Novel Direct Inverse Modeling Approach for Hysteresis Compensation of Piezoelectric Actuator in Feedforward Applications,” IEEE/ASME Trans. Mech., 18(3), pp. 981–989. [CrossRef]
Zhong, J., and Yao, B., 2008, “Adaptive Robust Precision Motion Control of a Piezoelectric Positioning Stage,” IEEE Trans. Control Syst. Technol., 16(5), pp. 1039–1046. [CrossRef]
Liaw, H. C., and Shirinzadeh, B., 2011, “Robust Adaptive Constrained Motion Tracking Control of Piezo-Actuated Flexure-Based Mechanisms for Micro/Nano Manipulation,” IEEE Trans. Ind. Electron., 58(4), pp. 1406–1415. [CrossRef]
Chen, G., Liu, X., and Du, Y., 2011, “Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges,” ASME J. Mech. Des., 133(8), p. 081002. [CrossRef]
Tian, Y., Shirinzadeh, B., and Zhang, D., 2010, “Closed-Form Compliance Equations of Filleted V-Shaped Flexure Hinges for Compliant Mechanism Design,” Precis. Eng., 34(3), pp. 408–418. [CrossRef]
Lobontiu, N., and Garcia, E., 2005, “Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms,” ASME J. Mech. Des., 127(4), pp. 766–773. [CrossRef]
Yong, Y. K., and Lu, T.-F., 2009, “Kinetostatic Modeling of 3-RRR Compliant Micro-Motion Stages with Flexure Hinges,” Mech. Mach. Theory, 44(6), pp. 1156–1175. [CrossRef]
Tian, Y., Shirinzadeh, B., and Zhang, D., 2009, “A Flexure-Based Five-Bar Mechanism for Micro/Nano Manipulation,” Sens. Actuators, A, 153(1), pp. 96–104. [CrossRef]
Choi, S. B., Han, S. S., Han, Y. M., and Thompson, B. S., 2007, “A Magnification Device for Precision Mechanisms Featuring Piezoactuators and Flexure Hinges: Design and Experimental Validation,” Mech. Mach. Theory, 42(9), pp. 1184–1198. [CrossRef]
Tian, Y., Shirinzadeh, B., Zhang, D., and Alici, G., 2009, “Development and Dynamic Modelling of a Flexure-Based Scott-Russell Mechanism for Nano-Manipulation,” Mech. Syst. Signal Process., 23(3), pp. 957–978. [CrossRef]
Ha, J.-L., Kung, Y.-S., Hu, S.-C., and Fung, R.-F., 2006, “Optimal Design of a Micro-Positioning Scott-Russell Mechanism by Taguchi Method,” Sens. Actuators A, 125(2), pp. 565–572. [CrossRef]
Chang, S. H., and Du, B. C., 1998, “A Precision Piezodriven Micropositioner Mechanism with Large Travel Range,” Rev. Sci. Instrum., 69(4), pp. 1785–1791. [CrossRef]
Hwang, D., Byun, J., Jeong, J., and Lee, M. G., 2011, “Robust Design and Performance Verification of an in-Plane XYθ Micropositioning Stage,” IEEE Trans. Nanotechnol., 10(6), pp. 1412–1423. [CrossRef]
Wu, Y., and Zhou, Z., 2004, “An XYθ Mechanism Actuated by One Actuator,” Mech. Mach. Theory, 39(10), pp. 1101–1110. [CrossRef]
Lobontiu, N., and Garcia, E., 2003, “Analytical Model of Displacement Amplification and Stiffness Optimization for a Class of Flexure-Based Compliant Mechanisms,” Comput. Struct., 81(32), pp. 2797–2810. [CrossRef]
Xu, Q., and Li, Y., 2011, “Analytical Modeling, Optimization and Testing of a Compound Bridge-Type Compliance Displacement Amplifier,” Mech. Mach. Theory, 46(2), pp. 183–200. [CrossRef]
Secord, T., and Asada, H. H., 2010, “A Variable Stiffness PZT Actuator Having Tunable Resonant Frequencies,” IEEE Trans. Rob., 26(6), pp. 993–1005. [CrossRef]
Liaw, H. C., Shirinzadeh, B., and Smith, J., 2008, “Robust Motion Tracking Control of Piezo-Driven Flexure-Based Four-Bar Mechanism for Micro/Nano Manipulation,” Mechatronics, 18(2), pp. 111–120. [CrossRef]
Ouyang, P. R., Zhang, W. J., and Gupta, M. M., 2008, “A New Compliant Mechanical Amplifier Based on a Symmetric Five-Bar Topology,” ASME J. Mech. Des., 130(10), p. 104501. [CrossRef]
Li, Y., and Xu, Q., 2010, “Development and Assessment of a Novel Decoupled XY Parallel Micropositioning Platform,” IEEE/ASME Trans. Mech., 15(1), pp. 125–135. [CrossRef]
Qin, Y., Shirinzadeh, B., Tian, Y., and Zhang, D., 2013, “Design Issues in a Decoupled XY Stage: Static and Dynamics Modeling, Hysteresis Compensation, and Tracking Control,” Sens. Actuators, 194, pp. 95–105. [CrossRef]
Polit, S., and Dong, J., 2011, “Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-/Nanomanufacturing,” IEEE/ASME Trans. Mech., 16(4), pp. 724–733. [CrossRef]
Yao, Q., Dong, J., and Ferreira, P. M., 2007, “Design, Analysis, Fabrication and Testing of a Parallel-Kinematic Micropositioning Xy Stage,” Int. J. Mach. Tools Manuf., 47(6), pp. 946–961. [CrossRef]
Qin, Y., Shirinzadeh, B., Tian, Y., Zhang, D., and Bhagat, U., “Design and Computational Optimization of a Decoupled 2-DOF Monolithic Mechanism,” IEEE/ASME Trans. Mech., (in press). [CrossRef]
Tian, Y., Shirinzadeh, B., and Zhang, D., 2010, “Design and Dynamics of a 3-DOF Flexure-Based Parallel Mechanism for Micro/Nano Manipulation,” Microelectron. Eng., 87(2), pp. 230–241. [CrossRef]
Dong, J., Yao, Q., and Ferreira, P. M., 2008, “A Novel Parallel-Kinematics Mechanism for Integrated, Multi-Axis Nanopositioning—Part 2: Dynamics, Control and Performance Analysis,” Precis. Eng., 32(1), pp. 20–33. [CrossRef]
Paros, J. M., and Weisbord, L., 1965, “How to Design Flexure Hinges,” Mach. Des., 37(27), pp. 151–156.
Wu, Y., and Zhou, Z., 2002, “Design Calculations for Flexure Hinges,” Rev. Sci. Instrum., 73(8), pp. 3101–3106. [CrossRef]
Qin, Y., Shirinzadeh, B., Zhang, D., and Tian, Y., 2013, “Compliance Modeling and Analysis of the Statically Indeterminate Symmetric Flexure Structure,” Precis. Eng., 37(2), pp. 415–424. [CrossRef]
Fung, R.-F., Weng, M.-H., and Kung, Y.-S., 2009, “FPGA-Based Adaptive Backstepping Fuzzy Control for a Micro-Positioning Scott-Russell Mechanism,” Mech. Syst. Signal Process., 23(8), pp. 2671–2686. [CrossRef]


Grahic Jump Location
Fig. 1

Scott-Russell mechanism: (a) schematic diagram, (b) a conventional flexure-based SR mechanism, and (c) deformation under a force actuation

Grahic Jump Location
Fig. 2

The first three mode shapes of the SR and ISR mechanisms: (a1)–(a3) SR mechanism, (b1)–(b3) ISR mechanism candidate 1, and (c1)–(c3) ISR mechanism candidate 2

Grahic Jump Location
Fig. 3

Candidates of the ISR mechanisms: (a) candidate 1: integrating prismatic joint into the drive point and (b) candidate 2: integrating prismatic joint into the output point

Grahic Jump Location
Fig. 4

Structural design of the 3-DOF manipulator: (a) schematic diagram and (b) kinematics model

Grahic Jump Location
Fig. 5

Kinematics model of the simplified 3-PRR manipulator

Grahic Jump Location
Fig. 6

Reachable workspace of the 3-DOF manipulator: (a) 3D workspace envelope and (b) sliced sections at different θ values

Grahic Jump Location
Fig. 9

Sliced sections of the reachable workspace obtained in computational analyses (Dotted lines show the corresponding analytical results)

Grahic Jump Location
Fig. 8

Response of the central platform with the second kinematic chain activated: (a) linear displacements and (b) angular displacement

Grahic Jump Location
Fig. 7

First three mode shapes of the 3-DOF manipulator with no PEA installed



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In