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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2016, Vol. 11 Issue (2) : 184-194    https://doi.org/10.1007/s11465-016-0385-y
RESEARCH ARTICLE
Analysis of suitable geometrical parameters for designing a tendon-driven under-actuated mechanical finger
Francesco PENTA,Cesare ROSSI(),Sergio SAVINO
Department of Industrial Engineering, University of Naples “Federico II”, Naples 80125, Italy
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Abstract

This study aims to optimize the geometrical parameters of an under-actuated mechanical finger by conducting a theoretical analysis of these parameters. The finger is actuated by a flexion tendon and an extension tendon. The considered parameters are the tendon guide positions with respect to the hinges. By applying such an optimization, the correct kinematical and dynamical behavior of the closing cycle of the finger can be obtained. The results of this study are useful for avoiding the snap-through and the single joint hyperflexion, which are the two breakdowns most frequently observed during experimentation on prototypes. Diagrams are established to identify the optimum values for the tendon guides position of a finger with specified dimensions. The findings of this study can serve as guide for future finger design.
Keywords tendon-driven fingers      mechanical finger design      under-actuated mechanical systems     
Corresponding Author(s): Cesare ROSSI   
Online First Date: 25 May 2016    Issue Date: 29 June 2016
 Cite this article:   
Francesco PENTA,Cesare ROSSI,Sergio SAVINO. Analysis of suitable geometrical parameters for designing a tendon-driven under-actuated mechanical finger[J]. Front. Mech. Eng., 2016, 11(2): 184-194.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-016-0385-y
https://academic.hep.com.cn/fme/EN/Y2016/V11/I2/184
Fig.1  Prospective view of the hand mechanism
Fig.2  Snap-through of an under-actuated finger: (a) Equilibrium curves, (b) finger deformed configurations, (c) traction vs. free end displacement of the flexural tendon
Fig.3  Hyperextension of an under-actuated finger. (a) Diagram of the tendon traction arm ratios vs. the phalanx rotations; (b) finger deformed configurations
Fig.4  Configuration of the finger: (a) Reference or initial configuration; (b) deformed configuration
Fig.5  Configurations of the ith joint: (a) Initial; (b) deformed
Fig.6  Diagrams of the ratios β ′ β (solid lines) and β ′ ‾ β ‾ (dashed lines) vs. the relative rotation φ
Fig.7  Diagrams of the ratios β ′ β (solid lines) and λ ′ Δ λ + β ′ ‾ β ‾ (dashed lines) vs. the relative rotation φ
Fig.8  Stability domains of fingers with similar joints
Fig.9  Diagrams of the ratios β ′ β (solid) and β ‾ ′ β ‾ (dashed) vs. the relative rotation φ
Fig.10  Diagrams of the limit shape parameter ε ¯
φ‾ e* ε‾
e=0.25e* e=0.5e* e=0.75e*
0 1.000 0.250 0.50 0.750
p/24 0.988 0.928 0.796 0.565
p/12 0.965 0.875 0.720 0.478
p/6 0.866 0.737 0.564 0.334
p/4 0.500 0.387 0.268 0.139
Tab.1  Limit values of the shape parameter ε ‾ for F=p/2
φ‾ e* ε‾
e=0.25e* e=0.5e* e=0.75e*
0 0.866 0.737 0.564 0.334
p/24 0.793 0.657 0.487 0.275
p/12 0.707 0.571 0.411 0.224
p/6 0.500 0.388 0.268 0.139
p/4 0.259 0.196 0.132 0.066
Tab.2  Limit values of the shape parameter ε ‾ for F=2p/3
Fig.11  Equilibrium curves of fingers with φ=π/2: (a) Joint geometries with decreasing arm ratios; (b) joint with increasing arm-ratios with φ ‾ =0; (c) joint with increasing arm-ratios with φ ¯ = π / 12 ; (d) joint with increasing arm-ratios with φ ¯ = π / 3
Fig.12  Equilibrium curves of fingers with φ=2π/3: (a) Joint geometries with decreasing arm ratios with φ ¯ = π / 3 ; (b)joint with increasing arm-ratios with φ ‾ =0; (c) joint with increasing arm-ratios with φ ¯ = π / 12 ; (d) joint with increasing arm-ratios with φ ¯ = π / 4
biDistance of the free path zi from the axis of the joint i—Arm of the flexural moment at the joint i
b‾iDistance of the free path li from the axis of the joint i—Arm of the extensor moment at the joint i
diDistances of the end sections of the flexural tendon guides on the right of the joint i
di−Distances of the end sections of the extensor tendon guides on the right of the joint i
fLoad applied to the flexural tendon
kStiffness of the spring
siDistances of the end sections of the flexural tendon guides on the left of the joint i
si ¯Distances of the end sections of the extensor tendon guides on the left of the joint i
uDisplacement of the free end of the flexural tendon
zi? Lengths of the free path followed by flexural tendon close to the joint i
liLengths of the free path followed by extensor tendon close to the joint i
βi=bi/siNormalized arm of the flexural moment
β‾i=b‾i/s‾iNormalized arm of the extensor moment
ΔziShortening of the free path zi
ΔlElongation of the extensor spring
εi, ε‾iShape parameters of the ith joint
εl ¯Limit value of ε‾
φ1Absolute rotation of the proximal phalanx.
φ2Relative rotation between the medial and proximal phalanxes
φ3Relative rotation between between the distal and medial phalanxes.
φiInitial angles between the distances si and di
φi−Initial angles between the distances s‾i and d‾i
λi=li/s‾iNormalized length of the extensor tendon free path at the joint i
ςi=zi/siNormalized length of the flexural tendon free path at the joint i
Tab.1  
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