Optimum design and preliminary experiments of a novel parallel end traction apparatus for upper-limb rehabilitation

doi:10.1007/s11465-021-0651-5

Front. Mech. Eng.

2021, Vol. 16

Issue (4) : 726-746 https://doi.org/10.1007/s11465-021-0651-5

RESEARCH ARTICLE

Optimum design and preliminary experiments of a novel parallel end traction apparatus for upper-limb rehabilitation

Shiping ZUO, Jianfeng LI, Mingjie DONG(

), Guotong LI, Yu ZHOU

Beijing Key Laboratory of Advanced Manufacturing Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China

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Abstract

Robot-assisted technology has been increasingly employed in the therapy of post stroke patients to deliver high-quality treatment and alleviate therapists’ burden. This paper introduces a novel parallel end traction apparatus (PETA) to supplement equipment selection. Considering the appearance and performance of the PETA, two types of special five-bar linkage mechanisms are selected as the potential configurations of the actuation execution unit because of their compact arrangement and parallel structure. Kinematic analysis of each mechanism, i.e., position solutions and Jacobian matrix, is carried out. Subsequently, a comparative study between the two mechanisms is conducted. In the established source of nondimensional parameter synthesis, the singularity, maximum continuous workspace, and performance variation trends are analyzed. Based on the evaluation results, the final scheme with determined configuration and corresponding near-optimized nondimensional parameters is obtained. Then, a prototype is constructed. By adding a lockable translational degree of freedom in the vertical direction, the PETA can provide 2D planar exercise and 3D spatial exercise. Finally, a control system is developed for passive exercise mode based on the derived inverse position solution, and preliminary experiments are performed to verify the applicability of the PETA.

Keywords parallel mechanism upper-limb rehabilitation singularity and workspace analyses performance evaluation optimum design

Corresponding Author(s): Mingjie DONG

Just Accepted Date: 23 September 2021 Online First Date: 16 November 2021 Issue Date: 28 January 2022

Cite this article:

Shiping ZUO,Jianfeng LI,Mingjie DONG, et al. Optimum design and preliminary experiments of a novel parallel end traction apparatus for upper-limb rehabilitation[J]. Front. Mech. Eng., 2021, 16(4): 726-746.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0651-5
https://academic.hep.com.cn/fme/EN/Y2021/V16/I4/726

Fig.1 Configurations of the (a) two-bar linkage mechanism, (b) RPRPR five-bar linkage mechanism, (c) symmetrical 5R five-bar linkage mechanism, (d) SPTM, and (e) SSTM.

Fig.2 Entire configurations of PETA with (a) SSTM and (b) SPTM as configuration of actuation execution units.

Fig.3 Parametric description of (a) SSTM and (b) SPTM.

Fig.4 End locus when a = 0 and the corresponding inverse position solution.

Fig.5 End loci when (a) a_p1 = 0 and (b) a_p2 = 0, and the corresponding inverse position solutions.

Fig.6 Source of nondimensional parameter synthesis of SSTM and SPTM.

Fig.7 Three representative schemes of each mechanism. (a) Scheme I, (b) Scheme II, and (c) Scheme III. Left: SSTM; right: SPTM.

Fig.8 Singular configurations of SSTM when (a) l₁ < l₂, (b) l₁ = l₂, and (c) l₁ > l₂.

Fig.9 Singular configurations of SPTM when (a) l₁≠ l₂ and (b) l₁ = l₂.

Fig.10 Singular loci and circle boundaries of (a) Scheme I, (b) Scheme II, and (c) Scheme III of SSTM; singular loci and circle boundaries of (d) Scheme I, (e) Scheme II, and (f) Scheme III of SPTM.

Fig.11 MCWs of (a) Scheme I, (b) Scheme II, and (c) Scheme III of SSTM. MCWs of (d) Scheme I, (e) Scheme II, and (f) Scheme III of SPTM.

Fig.12 Trends in values of G_ηJ of (a) SSTM and (b) SPTM with respect to values of l₁ and l₂.

Fig.13 Motion isotropy performances of (a) Scheme I, (b) Scheme II, and (c) Scheme III of SSTM. Motion isotropy performances of (d) Scheme I, (e) Scheme II, and (f) Scheme III of SPTM.

Fig.14 Mapping relationship between T_τ and T_f.

Fig.15 Trends in values of G_ris of (a) SSTM and (b) SPTM with respect to values of l₁ and l₂

Fig.16 Maximum force performances of (a) Scheme I, (b) Scheme II, and (c) Scheme III of SSTM. Maximum force performances of (d) Scheme I, (e) Scheme II, and (f) Scheme III of SPTM.

Fig.17 Trends in values of G_ηS of (a) SSTM and (b) SPTM with respect to values of l₁ and l₂.

Fig.18 Structural stiffness performances of (a) Scheme I, (b) Scheme II, and (c) Scheme III of SSTM. Structural stiffness performances of (d) Scheme I, (e) Scheme II, and (f) Scheme III of SPTM.

Fig.19 RTTA of actuation execution unit.

Fig.20 Calculation of mechanical limits (i.e., angle variation ranges of θ₁, θ₂, θ₈, and θ₉) of PETA.

Tab.1 Parameters of PETA

Fig.21 Mechanical prototype of PETA. ① Servo motor, ② planetary reducer, ③ screw shaft–screw nut combination, ④ lifting platform, ⑤ right-angle reducer, ⑥ concentric long output shafts, ⑦ handgrip strength measurement transducer, ⑧ six-axis circular load cell, ⑨ control cabinet, ⑩ computer monitor, ? mechanical cover, and ? rollers.

Fig.22 Preliminary experiments of passive exercise. (a) Planar square exercise, (b) planar circular exercise, and (c) spatial “8-font” shaped exercise.

Abbreviations
DOF	Degree of freedom
MCW	Maximum continuous workspace
PETA	Parallel end traction apparatus
ROM	Range of motion
RTTA	Rectangular target treatment area
SPTM	Special parallelogram type mechanism
SSTM	Special symmetrical type mechanism
Variables
B_i	Coordinate of point B_i
D_i	DOFs permitted by joints
f₁	Output force along X-axis
f₂	Output force along Y-axis
f	Vector of output forces
F	DOFs of SSTM and SPTM
G_ris	Global maximum force index
G_ηJ	Global motion isotropy index
G_ηS	Global structural stiffness index
h	Number of joints
J_FoSPTM	Forward Jacobian matrix of SPTM
J_FoSSTM	Forward Jacobian matrix of SSTM
J_IoSPTM	Inverse Jacobian matrix of SPTM
J_IoSSTM	Inverse Jacobian matrix of SSTM
J_S	Stiffness Jacobian matrix
J_V	Velocity Jacobian matrix
J_VoSPTM	Velocity Jacobian matrix of SPTM
J_VoSSTM	Velocity Jacobian matrix of SSTM
K	Scalar matrix representing the stiffness of the active joints
k₁, k₂	Stiffness of of joints A₁ and A₂, respectively
l₁,l₂	Nondimensional form of L₁ andL₂, respectively
l_vlp	Length of long principal axis of velocity ellipsoid
l_vsp	Length of short principal axis of velocity ellipsoid
L	Average value of L₁ and L₂
L₁	Length of links A_iB_i of SSTM, lengths of links A₁B₁ and B₂P of SPTM
L₂	Length of links B_iP of SSTM, lengths of links A₂B₂ and B₁P of SPTM
n	Number of links
P	Coordinate of point P
$q ˙$	Vector of input velocities

r_is	Local maximum force index, i.e., radius of inscribed circle contained in T_f
T_f	Generalized set of output forces of end effector
T_τ	Set of allowable torques of active joints
$u ˙$	Vector of output velocities
v	Number of parallel redundant constraints
w	MCW of mechanism
X_P	Coordinate of point P in X-axis direction
$X ˙ P$	Output velocity in X-axis direction
Y_P	Coordinate of point P in Y-axis direction
$Y ˙ P$	Output velocity in Y-axis direction
η_J	Local motion isotropy index, i.e., inverse value of condition number of velocity ellipsoid
η_S	Local structural stiffness index, i.e., maximum micro deformation of end effector
θ₁	Input angle of joint A₁
$θ ˙ 1$	Input angular velocity of joint A₁
θ₂	Input angle of joint A₂
$θ ˙ 2$	Input angular velocity of joint A₂
λ	Number of common constraints
λ_i	Eigenvalues of matrix J_S^TJ_S
τ	Vector of driving torques
τ₁, τ₂	Driving torque of joints A₁ and A₂, respectively
τ_1max, τ_2max	Maximum torque applied by actuator on joints A₁ and A₂, respectively
Δq	Vector of virtual angular displacements associated with active joints
Δu	Vector of virtual deformations of end effector
ΔX_P, ΔY_P	Virtual deformation of end effector in X- and Y-axis directions, respectively
Δθ₁, Δθ₂	Virtual angular displacement associated with joint A₁ and A₂, respectively

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