Abstract
Transfemoral amputees (TAs) have difficulty in mobility during walking, such as restricted movement of lower extremity and body instability, yet few transfemoral prostheses have explored human-like multiple motion characteristics by simple structures to fit the kinesiology, biomechanics, and stability of human lower extremity. In this work, the configurations of transfemoral prosthetic mechanism are synthesized in terms of human lower-extremity kinesiology. A hybrid transfemoral prosthetic (HTP) mechanism with multigait functions is proposed to recover the gait functions of TAs. The kinematic and mechanical performances of the designed parallel mechanism are analyzed to verify their feasibility in transfemoral prosthetic mechanism. Inspired by motion—energy coupling relationship of the knee, a wearable energy-damper clutched device that can provide energy in knee stance flexion to facilitate the leg off from the ground and can impede the leg’s swing velocity for the next stance phase is proposed. Its co-operation with the springs in the prismatic pairs enables the prosthetic mechanism to have the energy recycling ability under the gait rhythm of the knee joint. Results demonstrate that the designed HTP mechanism can replace the motion functions of the knee and ankle to realize its multimode gait and effectively decrease the peak power of actuators from 94.74 to 137.05 W while maintaining a good mechanical adaptive stability.
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Abbreviations
- DoF:
-
Degree-of-freedom
- FF:
-
Foot-flat
- GRFt:
-
Ground reaction force
- HO:
-
Heel-off
- HS:
-
Heel-strike
- HTP:
-
Hybrid transfemoral prosthetic
- PM:
-
Parallel mechanism
- SW:
-
Swing
- TA:
-
Transfemoral amputee
- TO:
-
Toe-off
- TO-I:
-
Toe-off I
- TO-II:
-
Toe-off II
- WEDC:
-
Wearable energy-damper clutched
- ZMP:
-
Zero moment point
- a ax, j, a ay, j :
-
Acceleration of the foot along the x- and y-axis, respectively
- a i, x, b i, x :
-
x component element of points Ai and Bi in fixed frame, respectively (i = 1, 2)
- a i, y, b i, y :
-
y component element of point Ai and Bi in fixed frame, respectively (i = 1, 2)
- a i, z, b i, z :
-
z component element of point Ai and Bi in fixed frame, respectively (i = 1, 2)
- a i :
-
Position vector of Ai with respect to the fixed frame
- A :
-
Rotational angle around w-axis in w-u-w Euler angles (i = 1, 2, 3)
- B :
-
Rotational angle around u′-axis in w-u-w Euler angles
- b i :
-
Position vector of Bi with respect to the fixed frame (i = 1, 2, 3)
- b Pi :
-
Position vector of Bi with respect to the moving frame (i = 1, 2, 3)
- C(ρ j, t):
-
Energy function is the optimization objective
- d ci :
-
Compressed distances of ith prismatic pairs (i = 1, 2)
- E :
-
Total momentum of TAs
- F ax, j, F ay, j :
-
Resulting forces along the x and y axes in the jth state case, respectively
- F cfi :
-
Elastic forces generated by the compression springs (i = 1, 2)
- f gi :
-
Force components of Fgi in heel-strike, foot-flat and toe-off phases (i = 1, 2, 3)
- F g :
-
Ground reaction force on right heel
- F gi :
-
Ground reaction force in heel-strike, foot-flat and toe-off phases (i = 1, 2, 3)
- g :
-
Gravitational acceleration
- g = (0, 0, −g)T :
-
Gravitational acceleration vector
- I a :
-
Inertia of the foot
- J :
-
Fully Jacobian matrix
- J k1n :
-
Kinematic Jacobian matrices of the nth UCU limbs (n = 1, 2)
- J cm :
-
mth constraint Jacobian matrices of RRR limbs (m = 1, 2, 3)
- J k2 :
-
Kinematic Jacobian matrices of RRR limbs
- k fi :
-
ith compression springs’ stiffness (i = 1, 2)
- k e :
-
Torsion spring’s stiffness
- k ij :
-
Unit vector of the jth revolute pair in the ith limb
- l i :
-
Length of the ith limb (i = 1, 2)
- \(\dot{l}_{i}\) :
-
Linear velocities of actuated joint in UCU limbs (i = 1, 2)
- L :
-
Total angular momentum of TAs
- M j :
-
Resulting moment exerted on the ankle joint
- ΔM ph1 :
-
Lack of hip flexor moment in the prosthetic system
- ΔM ph2 :
-
Extra hip extensor moment which endured by the transfemoral amputees
- ΔM pk1 :
-
Lack of knee extensor moment in the prosthetic system
- ΔM pk2 :
-
Lack of knee flexor moment in the prosthetic system
- ΔM pk3 :
-
Redundant knee extensor moment in the prosthetic system
- n gi :
-
Moment components of Fgi in heel-strike, foot-flat, and toe-off phases (i = 1, 2, 3)
- p x :
-
Position of ZMP in x direction
- p :
-
Position vector of the origin of moving frame with respect to the fixed frame
- R A B :
-
Transformation matrix from moving frame to the fixed frame
- R g :
-
Position vector of the ground reaction force with respect to the ZMP
- R m :
-
Position vector of the center of mass with respect to the global frame
- R p :
-
Position vector of the center of gravity with respect to ZMP
- s i :
-
Unit vector pointing along AiBi (i = 1, 2, 3)
- s j, i :
-
Unit vector of the jth joint in the ith limb (i = 1, 2 and j = 1, 2, …, 6; i = 3 and j = 1, 2, 3)
- T(ρ j, t):
-
Knee moment generated by optimized torsion spring
- Tg:
-
Moments generated from ground reaction force on right heel
- T(R p):
-
Resultant moment of GRF on the right heel with respect to ZMP
- V :
-
Optimized volumes
- V* :
-
Desired volumes
- x m, ẍ m :
-
Spatial position and acceleration of center of mass of human along x axis
- z m, \(\ddot{z}_{\rm{m}}\) :
-
Spatial position and acceleration of center of mass of human along z axis
- α j :
-
Angular acceleration of the foot around z axis in the jth state case
- α k :
-
Rotational angle of the knee flexion-extension
- β k :
-
Rotational angle of the ankle varus-valgus
- λ max, λ min :
-
Maximum and minimum eigenvalues of the fully Jacobian matrix, respectively
- ρ j :
-
Design variable
- ρ min :
-
Minimum density of the element to avoid the optimization singularity
- κ(J):
-
Condition number
- θ(t):
-
Knee extension angle
- \(\dot{\theta}(t)\) :
-
Angular acceleration
- \(\dot{\theta}_{3}\) :
-
Angular velocity of the actuated joint of RRR limb
- θ v :
-
Knee internal-external rotation angle
- Δθ kf1 :
-
Knee flexion increment in stance phase
- Δθ kf2 :
-
Difference between maximum plantar flexion and maximum dorsiflexion of ankle
- Δθ ke :
-
Knee extension angle increment in stance phase (here Δθke = Δθke1 in Fig. 1)
- Δθ ke(t):
-
Knee extension angle threshold
- Ω:
-
Design area
- Γ:
-
Rotational angle around w″-axis in w-u-w Euler Angles
- $ij :
-
jth kinematic screws in the ith limb (i = 1, j = 1, 2, …, 6)
- $3j :
-
jth kinematic screws in the 3rd limb (j = 1, 2, 3)
- $3jr :
-
jth constraint screws in the 3rd limb (j = 1, 2, 3)
- $k :
-
Kinematic screws set of moving platform
- $kj :
-
jth kinematic screw element in $k (j = 1, 2, 3)
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Acknowledgement
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51875033).
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Song, M., Guo, S., Oliveira, A.S. et al. Design method and verification of a hybrid prosthetic mechanism with energy-damper clutchable device for transfemoral amputees. Front. Mech. Eng. 16, 747–764 (2021). https://doi.org/10.1007/s11465-021-0644-4
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DOI: https://doi.org/10.1007/s11465-021-0644-4