Research Papers: Design of Mechanisms and Robotic Systems

Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation

[+] Author and Article Information
Jokin Aginaga

Institute of Smart Cities (ISC),
Public University of Navarre,
Iruñea-Pamplona 31006, Spain
e-mail: jokin.aginaga@unavarra.es

Xabier Iriarte

Institute of Smart Cities (ISC),
Public University of Navarre,
Iruñea-Pamplona 31006, Spain
e-mail: xabier.iriarte@unavarra.es

Aitor Plaza

Department of Mechanical,
Energetics and Materials Engineering,
Public University of Navarre,
Iruñea-Pamplona 31006, Spain
e-mail: aitor.plaza@unavarra.es

Vicente Mata

Centro de Investigación en Ingeniería Mecánica,
Universitat Politècnica de València,
Valencia 46022, Spain
e-mail: vmata@mcm.upv.es

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 31, 2017; final manuscript received April 18, 2018; published online July 3, 2018. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 140(9), 092304 (Jul 03, 2018) (12 pages) Paper No: MD-17-1521; doi: 10.1115/1.4040168 History: Received July 31, 2017; Revised April 18, 2018

Rehabilitation robots are increasingly being developed in order to be used by injured people to perform exercise and training. As these exercises do not need wide range movements, some parallel robots with lower mobility architecture can be an ideal solution for this purpose. This paper presents the design of a new four degree-of-freedom (DOF) parallel robot for knee rehabilitation. The required four DOFs are two translations in a vertical plane and two rotations, one of them around an axis perpendicular to the vertical plane and the other one with respect to a vector normal to the instantaneous orientation of the mobile platform. These four DOFs are reached by means of two RPRR limbs and two UPS limbs linked to an articulated mobile platform with an internal DOF. Kinematics of the new mechanism are solved and the direct Jacobian is calculated. A singularity analysis is carried out and the gained DOFs of the direct singularities are calculated. Some of the singularities can be avoided by selecting suitable values of the geometric parameters of the robot. Moreover, among the found singularities, one of them can be used in order to fold up the mechanism for its transportation. It is concluded that the proposed mechanism reaches the desired output movements in order to carry out rehabilitation maneuvers in a singularity-free portion of its workspace.

Copyright © 2018 by ASME
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Merlet, J. , 2006, Parallel Robots, Springer, Dordrecht, The Netherlands.
Neumann, K.-E. , 1988, “ Robot,” Parallel Kinematics Machines SL, U.S. Patent No. 4732525A. https://patents.google.com/patent/US4732525A/en
Zhang, D. , Bi, Z. , and Li, B. , 2009, “ Design and Kinetostatic Analysis of a New Parallel Manipulator,” Rob. Comput.-Integr. Manuf., 25(4–5), pp. 782–791. [CrossRef]
Chablat, D. , and Wenger, P. , 2003, “ Architecture Optimization of a 3-DOF Translational Parallel Mechanism for Machining Applications, the Orthoglide,” IEEE Trans. Rob. Autom., 19(3), pp. 403–410. [CrossRef]
Clavel, R. , 1990, “ Device for the Movement and Positioning of an Element in Space,” U.S. Patent No. 4976582A. https://patents.google.com/patent/US4976582A/en
Salgado, O. , Altuzarra, O. , Petuya, V. , and Hernández, A. , 2008, “ Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator,” ASME J. Mech. Des., 130(4), p. 042305. [CrossRef]
Briot, S. , and Bonev, I. A. , 2009, “ Pantopteron: A New Fully Decoupled 3DOF Translational Parallel Robot for Pick-and-Place Applications,” ASME J. Mech. Rob., 1(2), p. 021001. [CrossRef]
Company, O. , Pierrot, F. , Krut, S. , Baradat, C. , and Nabat, V. , 2011, “ Par2: A Spatial Mechanism for Fast Planar Two-Degree-of-Freedom Pick-and-Place Applications,” Meccanica, 46(1), pp. 239–248. [CrossRef]
Xie, F. , and Liu, X.-J. , 2015, “ Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform,” ASME J. Mech. Rob., 7(4), p. 041015. [CrossRef]
Kuo, C.-H. , and Dai, J. S. , 2012, “ Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery,” ASME J. Med. Devices, 6(2), p. 021008. [CrossRef]
Bi, Z. M. , 2013, “ Design of a Spherical Parallel Kinematic Machine for Ankle Rehabilitation,” Adv. Rob., 27(2), pp. 121–132. [CrossRef]
Chaker, A. , Mlika, A. , Laribi, M. A. , Romdhane, L. , and Zeghloul, S. , 2012, “ Synthesis of Spherical Parallel Manipulator for Dexterous Medical Task,” Front. Mech. Eng., 7(2), pp. 150–162. [CrossRef]
Plitea, N. , Szilaghyi, A. , and Pisla, D. , 2015, “ Kinematic Analysis of a New 5-DOF Modular Parallel Robot for Brachytherapy,” Rob. Comput. Integr. Manuf., 31, pp. 70–80. [CrossRef]
Jamwal, P. K. , Hussain, S. , and Xie, S. Q. , 2015, “ Review on Design and Control Aspects of Ankle Rehabilitation Robots,” Disability Rehabilitation: 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.
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. , Muccioli, G. M. 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]
Andriacchi, T. P. , Natarajan, R. , and Hurwitz, D. , 1997, “ Musculoskeletal Dynamics: Locomotion and Clinical Applications,” Basic Orthopaedic Biomechanics & Mechanobiology, Vol. 2, Lippincott Willians & Wikins, Philadelphia, PA, pp. 37–68.
Chen, W. , and Zhao, M. , 2001, “ A Novel 4-DOF Parallel Manipulator and Its Kinematic Modelling,” IEEE International Conference on Robotics and Automation (ICRA), Seoul, South Korea, May 21–26, pp. 3350–3355.
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]
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]
Altuzarra, O. , Macho, E. , Aginaga, J. , and Petuya, V. , 2015, “ Design of a Solar Tracking Parallel Mechanism With Low Energy Consumption,” Proc. Inst. Mech. Eng., Part C, 229(3), pp. 566–579. [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]
Kumar, N. , Piccin, O. , and Bayle, B. , 2014, “ A Task-Based Type Synthesis of Novel 2T2R Parallel Mechanisms,” Mech. Mach. Theory, 77, pp. 59–72. [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]
Ding, H. , ao Cao, W. , Chen, Z. , and Kecskeméthy, A. , 2015, “ Structural Synthesis of Two-Layer and Two-Loop Spatial Mechanisms With Coupling Chains,” Mech. Mach. Theory, 92, pp. 289–313. [CrossRef]
Wang, C. , Fang, Y. , and Fang, H. , 2017, “ Novel 2R3T and 2R2T Parallel Mechanisms With High Rotational Capability,” Robotica, 35(2), pp. 401–418. [CrossRef]
Araujo-Gómez, P. , Díaz-Rodríguez, M. , Mata, V. , Valera, A. , and Page, A. , 2016, “ Design of a 3-UPS-RPU Parallel Robot for Knee Diagnosis and Rehabilitation,” ROMANSY 21—Robot Design, Dynamics and Control, Vol. 569, CISM International Centre for Mechanical Sciences, Udine, Italy, pp. 303–310. [CrossRef]
Araujo-Gómez, P. , Mata, V. , Díaz-Rodríguez, M. , Valera, A. , and Page, A. , 2017, “ Design and Kinematic Analysis of a Novel 3 UPS/RPU Parallel Kinematic Mechanism With 2T2R Motion for Knee Diagnosis and Rehabilitation Tasks,” ASME J. Mech. Rob., 9(6), p. 061004. [CrossRef]
Nabat, V. , de la, O. , Rodríguez, M. , Company , O. Krut , S. , and Pierrot, V. , 2005, “ Par4: Very High Speed Parallel Robot for Pick-and-Place,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Edmonton, AB, Canada, Aug. 2–6, pp. 553–558.
Lambert, P. , and Herder, J. L. , 2015, “ A Novel Parallel Haptic Device With 7 Degrees of Freedom,” IEEE World Haptics Conference (WHC), Evanston, IL, June 22–26, pp. 183–188.
Hoevenaars, A. , Gosselin, C. , Lambert, P. , and Herder, J. , 2017, “ A Systematic Approach for the Jacobian Analysis of Parallel Manipulators With Two End-Effectors,” Mech. Mach. Theory, 109, pp. 171–194. [CrossRef]
Song, Y. , Qi, Y. , and Sun, T. , 2016, “ Conceptual Design and Kinematic Analysis of a Novel Parallel Manipulator With an Articulated Gripping Platform,” Advances in Reconfigurable Mechanisms and Robots II (Mechanism and Machine), X. Ding , X. Kong , and J. Dai , eds., Vol. 36, Springer International Publishing, Beijing, China, pp. 433–444. [CrossRef]
Gosselin, C. , and Angeles, J. , 1990, “ Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Wang, J. , and Gosselin, C. M. , 2004, “ Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms,” ASME J. Mech. Des., 126(1), pp. 109–118. [CrossRef]
Isaksson, M. , 2017, “ Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance,” ASME J. Mech. Des., 139(4), p. 042302. [CrossRef]
Aginaga, J. , Zabalza, I. , Altuzarra, O. , and Nájera, J. , 2012, “ Improving Static Stiffness of the 6-RUS Parallel Manipulator Using Inverse Singularities,” Rob. Comput.-Integr. Manuf., 28(4), pp. 458–471. [CrossRef]
Ma, O. , and Angeles, J. , 1991, “ Architecture Singularities of Platform Manipulators,” IEEE International Conference on Robotics and Automation (ICRA), Sacramento, CA, Apr. 9–11, pp. 1542–1547.
Joshi, S. A. , and Tsai, L.-W. , 2002, “ Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 254–258. [CrossRef]
St-Onge, B. M. , and Gosselin, C. M. , 2000, “ Singularity Analysis and Representation of the General Gough-Stewart Platform,” Int. J. Rob. Res., 19(3), pp. 271–288. [CrossRef]
Merlet, J. P. , 1999, “ Determination of 6D Workspaces of Gough-Type Parallel Manipulator and Comparison Between Different Geometries,” Int. J. Rob. Res., 18(9), pp. 902–916. [CrossRef]
Bonev, I. A. , and Ryu, J. , 2001, “ A Geometrical Method for Computing the Constant-Orientation Workspace of 6-PRRS Parallel Manipulators,” Mech. Mach. Theory, 36(1), pp. 1–13. [CrossRef]
Bonev, I. A. , and Ryu, J. , 2001, “ A New Approach to Orientation Workspace Analysis of 6-DOF Parallel Manipulators,” Mech. Mach. Theory, 36(1), pp. 15–28. [CrossRef]


Grahic Jump Location
Fig. 1

Illustration of the knee ligaments and bones

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Fig. 2

Movements of the required rehabilitation task

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Fig. 3

Schematic model of the 2-RPRR-2 UPS mechanism

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Fig. 4

View of the guides at the mobile platform

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Fig. 5

Preliminary CAD model of the mechanism: (a) with mobile platform and (b) without mobile platform

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Fig. 6

Individual movements of the output DOFs: (a) translation in x, (b) translation in z, (c) rotation about y, and (d) rotation about w

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Fig. 7

Definition of L, e, and r from the top view of the mechanism

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Fig. 8

Singular configuration with si⊥i,∀i

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Fig. 9

Singular configuration with horizontal actuators

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Fig. 10

Singular configuration with s1∥s3∥u

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Fig. 11

Singular configuration with parallel actuators

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Fig. 12

Singular configuration with intersection of actuators directions (I)

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Fig. 13

Singular configuration with intersection of actuators directions (II): (a) isometric view and (b) front view

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Fig. 14

Singular configuration with c2 = 0

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Fig. 15

Singular configuration with actuators 2 and 4 in vertical parallel planes

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Fig. 16

Platform in the fifth and sixth singularity configurations

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Fig. 17

Workspace of γ in terms of ((L/2−e)/r)

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Fig. 18

Singularities in the orientation workspace: (a) xp = 0 m, zp = 0.55 m and (b) xp = 0.2 m, zp = 0.55 m

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Fig. 19

Lack of singularities in the translation workspace: (a) φ = 0 rad, γ = 1.65 rad and (b) φ = 0.5 rad, γ = 1.65 rad

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Fig. 20

Rehabilitation trajectory in the xz plane

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Fig. 21

Values of input coordinates ρi along the trajectory



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