Keywords

1 Introduction

The current trend of industrial process automation requires extensive use of robots with different functional characteristics. Among them, the anthropomorphic robots and, in particular, the robotic hands, stand out due to their versatility.

The term “robot” was created in 1921 by Karel Čapek, a Czechoslovakian playwriter for his play “Rossum's Universal Robots”, where humans create mechanical devices to serve as workers. The term “robotics” was introduced by science fiction author Isaac Asimov in his 1942 short story “Runaround”, where he formulated his concept of “The Three Laws of Robotics” [1,2,3].

By the year 1950 engineers were developing machines to handle difficult or dangerous repetitive tasks for both defense and consumer manufacturing. Since robots were meant to replicate the pattern of motions that a human would make while lifting, pulling, pressing, or pushing, some of the designs were based on the anatomical structure of a human arm [1,2,3].

The functionality of these devices is still conditioned by the precision of the mechanical motions, which can be severely affected by the vibrations induced by various mechanical interactions [4,5,6,7].

This paper studies the vibrations of an anthropomorphic robotic hand that is to become part of a robot manipulator, intended for repetitive mechanical operation, for current use (Fig. 1).

Fig. 1.
figure 1

Robotic hand.

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The robotic hand is modeled as a system of elastic bodies with various geometric configurations and is analyzed from the vibratory point of view, using the CATIA V5 software.

2 Configuration of the Robotic Hand

The real human hand is a complex mechanism, made of 27 bones, out of which 19 can move relative to each other, therefore creating a mechanical system with 25 degrees of freedom [8, 9].

The practical implementation of a mechanical hand with a high number of degrees of freedom leads to major technological difficulties, such as: increasing the complexity of the system, using a high number of actuators and electronic control components, increasing the system mass, and need of large amounts of energy in order to operate.

As a result, robotic hands are often made in simpler configurations than those of a human hand, with a smaller number of mobilities, the motion of certain elements being correlated, by using additional connections. Such devices cannot perform motions as complex as those of a real hand, but they can provide a functional configuration close to the real one, enough for a large number of practical applications.

The studied device is such a simplified model, with only five mobilities (Fig. 2). The phalanges are modeled as elastic bodies connected by hinge joints.

Fig. 2.
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Robotic hand 3D model.

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The constructive characteristics of the studied robotic hand are presented in Fig. 3, while the material characteristics are given in Table 1.

Fig. 3.
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Constructive characteristics [mm] of finger I (left) and fingers II–V (right).

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Table 1. Material characteristics of the robotic hand elements
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3 Numerical Study and Results

The free vibrations of the robotic hand were analyzed using the CATIA V5 software, separately for the following case studies:

  1. 1.

    finger I (thumb), considered as an independent system (Fig. 4—left);

    Fig. 4.
    figure 4

    Finger I (left) and fingers II–V (right), considered as independent systems.

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  2. 2.

    one of the fingers II–V, which are presumed identical, considered as an independent system (Fig. 4—right);

  3. 3.

    the whole hand, considering the fingers fixed on the plate that models the carpals and metacarpals (Fig. 2).

    All three cases were analyzed for two configurations (Fig. 4), expressed by angle θ1 for the thumb and θ2 for the other finger:

    • extended phalanges (light gray)—θ1 = 0°, θ2 = 0°.

    • flexed phalanges (dark gray)—θ1 = 64°, θ2 = 32°.

Supplementary, the fingers as independent systems, were also considered in seven intermediate configurations between the above two, with the steps Δθ1 = 8° and Δθ2 = 4°, respectively.

Table 2 presents the first five eigenfrequencies[10] of the extended and flexed configurations.

Table 2. First five eigenfrequencies (Hz)
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Figure 5 illustrates the variation of the first two eigenfrequencies (f1 and f2) of the thumb and of the other finger, considered as independent systems, with respect to angle θ1 and θ2, respectively.

Fig. 5.
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Variation of the first two eigenfrequencies with respect to angles θ1 and θ2.

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Figures 6, 7, 8, 9, 10, 11, 12 and 13 illustrate some of the determined eigenmodes.

Fig. 6.
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Extended finger I (thumb)—eigenmodes 1, 2, 3.

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Fig. 7.
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Extended fingers II–V—eigenmodes 1, 2, 3.

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Fig. 8.
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Flexed finger I (thumb)—eigenmodes 1, 2, 3.

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Fig. 9.
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Flexed fingers II–V—eigenmodes 1, 2, 3.

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Fig. 10.
figure 10

Extended hand—eigenmode 1.

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Fig. 11.
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Extended hand—eigenmode 5.

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Fig. 12.
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Flexed hand—eigenmode 1.

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Fig. 13.
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Flexed hand—eigenmode 5.

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4 Conclusions

The vibratory analysis of the anthropomorphic robotic hand using the CATIA V5 software leads to the following conclusions:

  1. 1.

    the first eigenmode of all five fingers, considered as independent systems, is a bending one, in a plane parallel to that of the plate;

  2. 2.

    the second eigenmode of all five fingers, considered independent systems, is a bending one in a plane perpendicular to that of the plate;

  3. 3.

    the higher eigenmodes show coupled deformations and different aspects from one configuration to another; in some cases, the oscillations of the additional connections are prevailing;

  4. 4.

    the first two eigenfrequencies are higher for finger I (thumb), than for fingers II–V, which can be explained by the size difference between the first finger, which is smaller, and the other four. This is not valid for the higher modes, which can be explained by their different shape, from one configuration to another;

  5. 5.

    the first two eigenfrequencies, generally, tend to increase with the flexing degree (expressed by parameters θ1 and θ2, respectively), which is explained by the smaller general size of the system. This property is also not valid for higher eigenmodes;

  6. 6.

    for the first four eigenmodes of the hand, the bending of fingers II–V in a plane parallel to that of the plate is predominant, and the corresponding eigenfrequencies are very close in terms of values (coinciding at the displayed precision), due to the identical characteristics of the respective fingers; these modes correspond to the first vibration mode of fingers II–V, considered as independent systems;

  7. 7.

    for the fifth eigenmode of the hand, the bending of finger I (thumb) in a plane parallel to that of the plate is predominant; this mode corresponds to the first eigenmode of the finger I.

The above conclusions can be used for:

  • the design and the optimization of a robotic hand;

  • determining the optimal working parameters of such a device.