Mobile Mini-mechanism for Moving in Pipe with Small Diameter

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The above categorization is clear from the experience of the authors, and also from the inspiration of animal movements. Other ways of motion can be also realized by modifying these basic movements, or a combination thereof, but also is possible discovering new ways of motion. Thus, this division is not closed and this is subject to further research and development. In case of tubes with small diameter the minimal size of conventional drives used as an actuators limit the miniaturization. In addition the conventional wheel or caterpillar drive inclines to slipping, when inside wall is choked by dust. This study deals with mobile miniature mechanism, which utilizes energy released during crash of two masses. The diameter of realized miniature mechanism is 11 mm and its length is 35 mm. The impact force in moving direction is bigger than friction force between artificial hair and the tube wall. In inverse function the impact force is smaller than friction force ^{[1, 2, 3]}.

Figure 2. Global arrangement of miniature mechanism

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2. Mechanism Movement

Driving body of mobile mechanism in Figure 2consist of permanent magnet 4, magnetically circuit 2, 10. Driven body of mobile mechanism consist of electromagnet 3, adjusting module 6, recoil spring 8, guide rod 5, guide artificial hairs 7, power supply and sensing in moment of crash 9, contact wall of pipe 1. Cylindrically shaped permanent magnet 4 with longitudinal whole moves on guide rod 5 between electromagnet 3 and adjusting module 6. During crash of permanent magnet 4 and electromagnet 3 movement of mini-mechanism is created.

The movement analysis has been done on the simplifying model in Figure 3 ^[4].

Figure 3. Simplified model of the crash of drive and driven body

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According to theoretical analysis it is convenient to divide the miniature mechanism function into the three cycles, which interlock: 1. Preparing cycle, 2. Active cycle, 3. Regenerative cycle.

On the Figure 3 is x₁ – trajectory, v₁ – speed and m₁ – mass of drive body, and x₂ – trajectory, v₂ – speed and m₂ – mass of driven body. Also x_1P – distance between a centroid of drive body and spring of adjusting module if drive body is in contact with active surface, m_t – total mass of miniature mechanism, m_r – reduced mass of miniature mechanism, F₁ – friction force between drive body and sliding drive, F₂ – friction force between artificial hairs and tube wall, F_P – attractive force of drive body to the active surface of miniature mechanism, F_O – repulsive force between drive body and ative surface of miniature mechanism, F_h – drive force of miniature mechanism, T – time of miniature mechanism cycle, k – constant of the spring, which represents a deformation of drive and driven body during the crash on active surface.

According to nonlinearity of movement equations we have divided the analysis into the three phases. In every phase the friction is represented by Coulomb friction with absolute valve F_tr0 ^{[5, 6]}

2.1. Phase A

At the beginning of this phase the drive body is in the contact with miniature mechanism active surface in consequence of attractive force F_P. By the voltage impulse in the coil of electromagnet in time the repulsive force F_Ois activated and consequently the drive body is moving toward to the adjusting module. Duration of the repulsive force is till the moment of contact of drive body with spring on adjusting module. In this moment the Phase A is finished and Phase B begins ^[5].

2.2. Phase B

This phase begins in moment of contact of drive body with spring on adjusting module in moment and ends in moment of end of this this contact in time . In this phase only attractive force F_P influences on drive body. The absolute value of deformation force created as a result of impact between drive body with spring of adjusting module is smaller than absolute value of friction force F₂during this phase. It means, that miniature mechanism do not move.

2.3. Phase C

At the moment of end of contact of drive body in the Phase B in time the Phase C begins. During this phase the drive body is accelerated by attractive force F_Ptoward to the active surface of the miniature mechanism. In the moment of the contact with this surface in time this phase is finished and the Phase D of active cycle begins.

2.4. Phase D

This one begins in the moment of contact of drive and driven body on the active surface. Phase D is an immediate continuing of preparing cycle. Its duration begins by time of impact between drive and driven body in time and ends when drive impact force F_his equal to the friction force F₂in time . It means that driven body of miniature mechanism does not move in this phase yet.

2.5. Phase E

Beginning of this phase is in time when , and begins in time when drive force . During all this phase miniature mechanism moves.

2.6. Phase F

This phase follows immediately after the impact of drive and driven body on active force in time and ends in moment of miniature mechanism stopping in time , when the regenerative cycle begins.

3. Regenerative Cycle

The cycle has only one phase marked as G . Its duration is given by allowed operation temperature of miniature mechanism, which is created in conclusion of Joule loss in the coil of electromagnet ^{[9, 10]}. Time dependencies of speed v₂ and trajectory x₂ during active tact obtained by simulation are shown by Figure 4 and Figure 5. Parameters of miniature mechanism was chosen as follows:,,, According to fact that Phase D is very short, and it is impossible to show it separately, the Phases D and E are marked together. Duration of Phase D is only ^{[7, 8]}.

Figure 4. Time course of speed v₂ of driven body during active tact

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Figure 5. Time course of trajectory x₂ of driven body during active tact

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From analysis of miniature mechanism movement, which has been accomplished for simplified model on Fig. 3, driven body in every three phases of active cycle is described by motional equation:

(1)

By solving and modification of Equation 1 for speed of driven body we should obtain a relation:

(2)

(3)

which after omitting of friction force F₂ represents a known relation for direct impact of two elastic spheres, 1(t) is the Heaviside function. From Equation (2, 3) results, that time, in which the driven body is stopped, i.e. , is

(4)

For mean speed of miniature mechanism v_2strwe should write:

(5)

where T is time of miniature mechanism cycle:

(6)

4. Experimental Results

Because analytical expression of attractive and repulsive force dependence on distance l could by find analytically only for simple magnetic circuits, we examined them experimentally. The attractive force has been examined by spring force sensor in following way: for given distance l, we measured force, which could separate the drive body from electromagnet. The current through the coil was equal to zero. The measured data and regression dependence are show on Figure 6 ^{[7, 8]} .

Figure 6. Dependence of the driving-body attractive force on the distance from electromagnet

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The dependence of repulsive force on distance l was determined indirectly. According to fact, that attractive force could not be eliminated, we measured difference between attractive and repulsive force for given distance l. The drive body was weighted by known weight, while the current through the coil was constant. Similarly to previous we examined, which weight is able to separate the drive body from electromagnet. The Fig. 7 shows the measured data and regression dependence. Using these attractive and repulsive force dependencies we have made the model of mobile robot according to the Fig. 2. The weight of drive and driven body is 10 g. The speed of mobile robot in glass tube was 2 cm s^-1.

From performed analysis of miniature mechanism for moving in tube with small diameter following facts results ^{[6, 7]}:

Ÿ mean and immediate speed of miniature mechanism increases with increasing of momentum of drive body in moment of crash with driven body,

Ÿ momentum of drive body increases with increasing of constant J appearing in dependence for repulsive force. This constant depends on current size in coil of electromagnet,

Ÿ optimal position of spring depends only on character of repulsive force dependence. This is valid according to assumption that speed of drive body in moment of impact on spring is equal to the speed in moment of its bounce and repulsive force durates only till the impact with spring.

Figure 7. Dependence of the driving-body repulsive force on the distance from electromagnet

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