Prototype Fish Robot, UPF-2001Detail Information of Power UnitKoichi Hirata and Syusuke Kawai, November 26, 2001 Structure and CharacteristicsThe power unit of the fish robot, UPF-2001 consists of (i) a D/C motor as a power source, (ii) a gear mechanism for reducing the revolution of the motor, (iii) a Scotch-yoke mechanism to change from rotating motion to reciprocating motion, (iv) seal devices for waterproof, and (v) a connecting mechanism to a tail fin. Table 1 lists the specifications of the power unit.
_{G}(m/s) is calculated by the next equation.
_{Gmax}.
_{Gmax} is calculated by the next equation with the surface of the flat plate, S_{A}.
_{D} is drag coefficient (C_{D}=1.2), p is density of water (p=1000 kg/m^{3}. Then, the maximum torque, T_{qmax}(Nm) is caluculated by the next equation.
On the other hand, the torque of a final shaft of the motor becomes T
In order to keep stable motion of the tail fin, we need to calculate mean power (W). A simple method like the above calculation is shown in follows.
The center of gravity, G moves about 4rsinA(m) around one cycle. So, mean velosity, v
_{Gmax} of Eqs. (4) and (5) is replaced to the mean velosity, v_{m}, the mean force, F_{m} and the mean torque, T_{qm} are calculated by the next equations.
(8)
_{m}(W) is calculated by the next equation.
_{m}(W) of Eq. (9) is smaller than the power of the motor, the motor keeps to drive the tail fin with stable motion.
We can predict the torque and power with the above equations, and adopt specifications of the fish robot approximately. However, in the first design stage, we must decide the reduced ratio of the gear mechanism. As an example, we introduce a design flowchart for the reduced ratio.
In a catalog or an explanatory note of a R/C model motor, the specifications in the maximum power condition, the maximum efficiency condition and no-load condition as shown in Table 1. Each rotating speed and torque satisfy the next relations, with the rotating speed (Hz), f
(11)
_{P} equals to 1/2 of f_{N}. Also, in the case of the R/C model motor, f_{E} is very higher than f_{P}, and is near f_{N}. When such motor is adopted to a fish robot, the reduced ratio, D must be desided in the rated operation, that is in from f_{P} to f_{E} of the motor speed.
The relation between the frequency of the tail fin, f and the rotating speed of the motor, f
(13)
_{qmot}, f_{mot}, r, A, S_{A} and D with Eqs. (3)-(7). An example is the next equation.
_{A}=0.036 m^{2}) and the amplitude, A=10 deg. From this table, it was clalifed that 1/40 to 1/60 of the reduced ratio, D is suitable for the UPF-2001. After conciderations of the calculated results and location of the gears, we decided D=1/40.5.
Table 2. Calculated result for the reduced ratioClick figure, show a bigger one.
Calculated Result
Figure 8 shows the calculated results of the relation between the frequency, f and the maximum torque, T
Figure 9 shows the calculated results of the relation between the frequency, f and the mean power, W
From these calculated results, we consider that High torque type motor, Motor B (Tamiya, ACTO-POWER) is effective in the condition of bigger amplitude, high speed type motor, Motor C (Tamiya, DYNA-RUN) is effective in the condition of high frequency and smaller amplitude. And we think that the standard motor, Motor A (Mabuchi, RS-540SH) is effective a long-time operation, because it has small consumer energy.
ConclusionIn this web page, we introduced the power unit of the UPF-2001 and the simple method for the mechanical design. In the above calculation, the tail fin is replaced to a flat plate. However, the real fin has cone-shape, so it may be that the drag coeffcient is diffrent from the above calculation. Also, we wonder that the constant drag coefficient is suitable or not, because the swimming fish robot has a complex water flow. However we sure that the qualitative characteristics of the torque and the power, as shown in Eqs. (5) and (8), are suitable for the mechanical design.
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