Research Papers

Design and Kinematic Analysis of a Novel 3UPS/RPU Parallel Kinematic Mechanism With 2T2R Motion for Knee Diagnosis and Rehabilitation Tasks

[+] Author and Article Information
Pedro Araujo-Gómez

Laboratorio de Mecatrónica y Robótica,
Facultad de Ingeniería,
Universidad de los Andes,
Mérida 5101, Venezuela

Vicente Mata

Centro de Investigación en,
Ingeniería Mecánica,
Universitat Politècnica de València,
Valencia 46022, Spain

Miguel Díaz-Rodríguez

Laboratorio de Mecatrónica y Robótica,
Facultad de Ingeniería,
Universidad de los Andes,
Mérida 5101, Venezuela
e-mail: dmiguel@ula.ve

Angel Valera

Instituto Universitario de Automática,
e Informática Industrial,
Universitat Politècnica de València,
Valencia 46022, Spain

Alvaro Page

Grupo de Tecnología Sanitaria del IBV,
CIBER de Bioingeniería, Biomateriales,
y Nanomedicina (CIBER-BBN),
Universitat Politècnica de València,
Valencia 46022, Spain

1Corresponding author.

Manuscript received February 4, 2017; final manuscript received August 9, 2017; published online September 18, 2017. Assoc. Editor: Marcia K. O'Malley.

J. Mechanisms Robotics 9(6), 061004 (Sep 18, 2017) (10 pages) Paper No: JMR-17-1031; doi: 10.1115/1.4037800 History: Received February 04, 2017; Revised August 09, 2017

This paper proposes a two translational and two rotational (2T2R) four-degrees-of-freedom (DOF) parallel kinematic mechanism (PKM) designed as a knee rehabilitation and diagnosis mechatronics system. First, we establish why rehabilitation devices with 2T2R motion are required, and then, we review previously proposed parallel mechanisms with this type of motion. After that, we develop a novel proposal based on the analysis of each kinematic chain and the Grübler–Kutzbach criterion. Consequently, the proposal consists of a central limb with revolute-prismatic-universal (RPU) joints and three external limbs with universal-prismatic-spherical (UPS) joints. The Screw theory analysis verifies the required mobility of the mechanism. Also, closed-loop equations enable us to put forward the closed-form solution for the inverse-displacement model, and a numerical solution for the forward-displacement model. A comparison of the numerical results from five test trajectories and the solution obtained using a virtual prototype built in msc-adams shows that the kinematic model represents the mechanism's motion. The analysis of the forward-displacement problem highlights the fact that the limbs of the mechanism should be arranged asymmetrically. Moreover, the Screw theory makes it possible to obtain the Jacobian matrix which provides insights into the analysis of the mechanism's workspace. The results show that the proposed PKM can cope with the required diagnosis and rehabilitation task. The results provide the guidelines to build a first prototype of the mechanism which enables us to perform initial tests on the robot.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Qian, Z. , and Bi, Z. , 2015, “ Recent Development of Rehabilitation Robots,” Adv. Mech. Eng., 7(2), p. 563062. [CrossRef]
Robertson, J. , Jarrassé, N. , and Roby-Brami, A. , 2010, “ Rehabilitation Robots: A Compliment to Virtual Reality,” Schedae, 1(6), pp. 77–94.
Meng, W. , Liu, Q. , Zhou, Z. , Ai, Q. , Sheng, B. , and Xie, S. S. , 2015, “ Recent Development of Mechanisms and Control Strategies for Robot-Assisted Lower Limb Rehabilitation,” Mechatronics, 31, pp. 132–145. [CrossRef]
Jezernik, S. , Colombo, G. , Keller, T. , Frueh, H. , and Morari, M. , 2003, “ Robotic Orthosis Lokomat: A Rehabilitation and Research Tool,” Neuromodulation, 6(2), pp. 108–115. [CrossRef] [PubMed]
Veneman, J. F. , Kruidhof, R. , Hekman, E. E. , Ekkelenkamp, R. , Van Asseldonk, E. H. , and Van Der Kooij, H. , 2007, “ Design and Evaluation of the LOPES Exoskeleton Robot for Interactive Gait Rehabilitation,” IEEE Trans. Neural Syst. Rehabil. Eng., 15(3), pp. 379–386. [CrossRef] [PubMed]
Freivogel, S. , Mehrholz, J. , Husak-Sotomayor, T. , and Schmalohr, D. , 2008, “ Gait Training With the Newly Developed ‘LokoHelp’-System is Feasible for Non-Ambulatory Patients After Stroke, Spinal Cord and Brain Injury—A Feasibility Study,” Brain Inj., 22(7–8), pp. 625–632. [CrossRef] [PubMed]
Díaz, I. , Gil, J. J. , and Sánchez, E. , 2011, “ Lower-Limb Robotic Rehabilitation: Literature Review and Challenges,” J. Rob., 2011, p. 759764.
Riener, R. , Lunenburger, L. , Jezernik, S. , Anderschitz, M. , Colombo, G. , and Dietz, V. , 2005, “ Patient-Cooperative Strategies for Robot-Aided Treadmill Training: First Experimental Results,” IEEE Trans. Neural Syst. Rehabil. Eng., 13(3), pp. 380–394. [CrossRef] [PubMed]
Hesse, S. , Uhlenbrock, D. , and Sarkodie-Gyan, T. , 1999, “ Gait Pattern of Severely Disabled Hemiparetic Subjects on a New Controlled Gait Trainer as Compared to Assisted Treadmill Walking With Partial Body Weight Support,” Clin. Rehabil., 13(5), pp. 401–410. [CrossRef] [PubMed]
Wu, J. , Gao, J. , Song, R. , Li, R. , Li, Y. , and Jiang, L. , 2016, “ The Design and Control of a 3DOF Lower Limb Rehabilitation Robot,” Mechatronics, 33, pp. 13–22. [CrossRef]
Jia, X. , Che, J. , Liu, H. , Xiong, K. , and Huang, T. , 2017, “ Conceptual Design and Dimensional Synthesis of a Novel Parallel Mechanism for Lower-Limb Rehabilitation,” CCToMM Mechanisms, Machines, and Mechatronics (M3) Symposium, pp. 1–12.
Schmidt, H. , Werner, C. , Bernhardt, R. , Hesse, S. , and Krüger, J. , 2007, “ Gait Rehabilitation Machines Based on Programmable Footplates,” J. Neuroeng. Rehabil., 4(1), p. 2. [CrossRef] [PubMed]
Jamwal, P. K. , Hussain, S. , and Xie, S. Q. , 2015, “ Review on Design and Control Aspects of Ankle Rehabilitation Robots,” Disability Rehabil.: Assistive Technol., 10(2), pp. 93–101. [CrossRef]
Rastegarpanah, A. , Saadat, M. , and Borboni, A. , 2016, “ Parallel Robot for Lower Limb Rehabilitation Exercises,” Appl. Bionics Biomech., 2016, p. 8584735. [PubMed]
Vallés, M. , Cazalilla, J. , Valera, Á. , Mata, V. , Page, Á. , and Díaz-Rodríguez, M. , 2015, “ A 3-PRS Parallel Manipulator for Ankle Rehabilitation: Towards a Low-Cost Robotic Rehabilitation,” Robotica, 35(10), pp. 1939–1957.
Valera, A. , Díaz-Rodríguez, M. , Valles, M. , Oliver, E. , Mata, V. , and Page, A. , 2016, “ Controller–Observer Design and Dynamic Parameter Identification for Model-Based Control of an Electromechanical Lower-Limb Rehabilitation System,” Int. J. Control, 90(4), pp. 702–714. [CrossRef]
Mohan, S. , Mohanta, J. , Kurtenbach, S. , Paris, J. , Corves, B. , and Huesing, M. , 2017, “ Design, Development and Control of a 2PRP-2PPR Planar Parallel Manipulator for Lower Limb Rehabilitation Therapies,” Mech. Mach. Theory, 112, pp. 272–294. [CrossRef]
Escamilla, R. F. , MacLeod, T. D. , Wilk, K. E. , Paulos, L. , and Andrews, J. R. , 2012, “ Cruciate Ligament Loading During Common Knee Rehabilitation Exercises,” Proc. Inst. Mech. Eng., Part H, 226(9), pp. 670–680. [CrossRef]
Colombet, P. , Jenny, J. , Menetrey, J. , Plaweski, S. , and Zaffagnini, S. , 2012, “ Current Concept in Rotational Laxity Control and Evaluation in ACL Reconstruction,” Orthop. Traumatol.: Surg. Res., 98(8), pp. S201–S210. [CrossRef] [PubMed]
Alam, M. , Bull, A. M. , Thomas, R. D. , and Amis, A. A. , 2013, “ A Clinical Device for Measuring Internal-External Rotational Laxity of the Knee,” Am. J. Sports Med., 41(1), pp. 87–94. [CrossRef] [PubMed]
Höher, J. , Akoto, R. , Helm, P. , Shafizadeh, S. , Bouillon, B. , and Balke, M. , 2015, “ Rolimeter Measurements Are Suitable as Substitutes to Stress Radiographs in the Evaluation of Posterior Knee Laxity,” Knee Surg. Sports Traumatol. Arthroscopy, 23(4), pp. 1107–1112. [CrossRef]
Araujo-Gómez, P. , Díaz-Rodriguez, M. , Mata, V. , Valera, A. , and Page, A. , 2016, “ Design of a 3-UPS-RPU Parallel Robot for Knee Diagnosis and Rehabilitation,” 21st CISM-IFToMM Symposium, Udine, Italy, June 20–23, pp. 303–310.
Wiertsema, S. , Van Hooff, H. , Migchelsen, L. , and Steultjens, M. , 2008, “ Reliability of the KT1000 Arthrometer and the Lachman Test in Patients With an ACL Rupture,” Knee, 15(2), pp. 107–110. [CrossRef] [PubMed]
Lopomo, N. , Zaffagnini, S. , Signorelli, C. , Bignozzi, S. , Giordano, G. , Marcheggiani Muccioli, G. M. , and Visani, A. , 2012, “ An Original Clinical Methodology for Non-Invasive Assessment of Pivot-Shift Test,” Comput. Methods Biomech. Biomed. Eng., 15(12), pp. 1323–1328. [CrossRef]
Chen, W.-J. , Zhao, M.-Y. , Zhou, J.-P. , and Qin, Y.-F. , 2002, “ A 2T-2R, 4-DOF Parallel Manipulator,” ASME Paper No. DETC2002/MECH-34303.
Fan, C. , Liu, H. , Yuan, G. , and Zhang, Y. , 2011, “ A Novel 2T2R 4-DOF Parallel Manipulator,” IEEE Fourth International Symposium on Knowledge Acquisition and Modeling (KAM), Sanya, China, Oct. 8–9, pp. 5–8.
Fan, C. , Liu, H. , and Zhang, Y. , 2013, “ Type Synthesis of 2T2R, 1T2R and 2R Parallel Mechanisms,” Mech. Mach. Theory, 61, pp. 184–190. [CrossRef]
Xie, F. , Li, T. , and Liu, X. , 2013, “ Type Synthesis of 4-DOF Parallel Kinematic Mechanisms Based on Grassmann Line Geometry and Atlas Method,” Chin. J. Mech. Eng., 26(6), pp. 1073–1081. [CrossRef]
Ghaffari, H. , Payeganeh, G. , and Arbabtafti, M. , 2014, “ Kinematic Design of a Novel 4-DOF Parallel Mechanism for Turbine Blade Machining,” Int. J. Adv. Manuf. Technol., 74(5–8), pp. 729–739. [CrossRef]
Gan, D. , Dai, J. S. , Dias, J. , Umer, R. , and Seneviratne, L. , 2015, “ Singularity-Free Workspace Aimed Optimal Design of a 2T2R Parallel Mechanism for Automated Fiber Placement,” ASME J. Mech. Rob., 7(4), p. 041022. [CrossRef]
Merlet, J.-P. , 2000, Parallel Robots, Vol. 128, Kluwer Academic Publishers, Norwell, MA. [CrossRef] [PubMed] [PubMed]
Tsai, L.-W. , 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley, New York.
Paul, R. P. , 1981, Robot Manipulators: Mathematics, Programming, and Control: The Computer Control of Robot Manipulators, MIT Press, Cambridge, MA.
Zhao, J.-S. , Zhou, K. , and Feng, Z.-J. , 2004, “ A Theory of Degrees of Freedom for Mechanisms,” Mech. Mach. Theory, 39(6), pp. 621–643. [CrossRef]
Wang, L. , Xu, H. , and Guan, L. , 2015, “ Mobility Analysis of Parallel Mechanisms Based on Screw Theory and Mechanism Topology,” Adv. Mech. Eng., 7(11), pp. 1–13.
Hunt, K. H. , 1986, “ Special Configurations of Robot-Arms Via Screw Theory,” Robotica, 4(3), pp. 171–179. [CrossRef]
Gosselin, C. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Merlet, J.-P. , 1989, “ Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Rob. Res., 8(5), pp. 45–56. [CrossRef]
Gibson, C. , and Hunt, K. , 1990, “ Geometry of Screw Systems—1: Screws: Genesis and Geometry,” Mech. Machine Theory, 25(1), pp. 1–10. [CrossRef]
Zlatanov, D. , Fenton, R. , and Benhabib, B. , 1998, “ Identification and Classification of the Singular Configurations of Mechanisms,” Mech. Mach. Theory, 33(6), pp. 743–760. [CrossRef]
Andriacchi, T. P. , Natarajan, R. , and Hurwitz, D. , 1997, “ Musculoskeletal Dynamics, Locomotion, and Clinical Applications,” Basic Orthopedic Biomechanics & Mechano Biology, Lippincott Willians & Wikins, Philadelphia, PA, pp. 91–121.


Grahic Jump Location
Fig. 1

Movements to be carried out by the PKM

Grahic Jump Location
Fig. 2

Modified 2T2R parallel mechanisms, and the two proposed novel mechanisms: (a) 2PRS + 2PUS, (b) 2RPU + 2SPS, (c) 2PCUP + PRC + PPU, (d) [2RPC + 2SPS, (e) RPS + 3UPS, and (f) PRS + 3PUS

Grahic Jump Location
Fig. 3

Link frame location for one external limb, including U-joint rotations and P-joint displacement. Link frame rotation for the central limb, including R-joint rotation and P-joint displacement. (a) Schematic representation of the 3UPS/RPU PKM and (b) link frame locations of the UPS and the UPS limbs, Paul notation [33].

Grahic Jump Location
Fig. 4

Screw axis for the RPU limb

Grahic Jump Location
Fig. 5

Closed-loops of the PKM

Grahic Jump Location
Fig. 6

Virtual prototype built in msc-adams

Grahic Jump Location
Fig. 7

Simulation of a rehabilitation task

Grahic Jump Location
Fig. 8

Workspace of the 3-UPS/1RPU mechanism

Grahic Jump Location
Fig. 9

Prototype of the 3UPS/RPU for knee diagnosis and rehabilitation

Grahic Jump Location
Fig. 10

Cartesian reference and actual robot response



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