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.
Distance of the free path zi from the axis of the joint i—Arm of the flexural moment at the joint i
b‾i
Distance of the free path li from the axis of the joint i—Arm of the extensor moment at the joint i
di
Distances 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
f
Load applied to the flexural tendon
k
Stiffness of the spring
si
Distances 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
u
Displacement of the free end of the flexural tendon
zi?
Lengths of the free path followed by flexural tendon close to the joint i
li
Lengths of the free path followed by extensor tendon close to the joint i
βi=bi/si
Normalized arm of the flexural moment
β‾i=b‾i/s‾i
Normalized arm of the extensor moment
Δzi
Shortening of the free path zi
Δl
Elongation of the extensor spring
εi,ε‾i
Shape parameters of the ith joint
εl¯
Limit value of ε‾
φ1
Absolute rotation of the proximal phalanx.
φ2
Relative rotation between the medial and proximal phalanxes
φ3
Relative rotation between between the distal and medial phalanxes.
φi
Initial angles between the distances si and di
φi−
Initial angles between the distances s‾iand d‾i
λi=li/s‾i
Normalized length of the extensor tendon free path at the joint i
ςi=zi/si
Normalized length of the flexural tendon free path at the joint i
Tab.1
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