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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

Professor
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.

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Figures

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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