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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.

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Figures

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

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