Introduction and Project Background
- We are simplifying the traditional undulating fin robot design by utilizing a central camshaft instead of a large number of servos. Below are two examples of previous undulating fin robots that utilize more robust motor control rather than pure mechanical power transmission.
- We follow a similar structure to the figure shown below, where we chose to utilize a common CAM shaft that drives each part of the fin.
Requirements and Specifications
Qualitative
-
Moves in water and on land
- This is the main purpose of our project
- The fins allow for both thrust in water and rolling friction on land
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Waterproof
- Electronics need a dry environment
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Floats
- We want a surface-operating robot that doesn't need to adjust buoyancy
- Looks swag and fishy
Quantitative
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Tip of fins move 2 inches peak to peak
- Realistic distance we need the fin to move to generate enough thrust in water and enough distance to reach over obstacles on land
- The original goal was 4 inches but had to pivot due to geometric constraints. The fin rod pivot point must be at the hull/water interface and the hull must be a certain width for stability.
- CAM follower moves 1 inch peak to peak
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Camshaft rotates at 60rpm
- Creates a realistic and effective undulating frequency for water and land
Design Features of Main Subsystems
Significant Design Decisions
-
Cam shaft
- We opted for a camshaft to create a simplified version of the more common servo based undulating fin robot. Using a servo for each fin rod adds control complexity and greater chance for failure. Using a single central camshaft leads to a more mechanically robust and simple robot.
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Cam geometry
- We chose a specific cam geometry to create the sinusoidal motion of the fins
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Fin rod pivot geometry
- We designed a slotted hole for the pivot at the hull/water interface that restricts the vertical and horizontal translation of the fin rods while allowing to pitch back and forth
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Follower to fin rod connection
- We decided to machine a halved pivot joint to connect the fin rods to the followers. This helps reduce our part count as we only need a bolt and nut to attach the two as opposed to some other specialized connector.
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ESP for WiFi control
- A simple ESP32 microcontroller was implemented so that the vehicle can move autonomously over WiFi, taking out the need for long wires to be attached to a separate microprocessor
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Fin rod pivot point location
- Due to size constraints the maximum amplitude of the follower motion was highly limited. To achieve our quantitative specification of 2 inches of fin rod tip motion, the pivot point of the fin rod was strategically placed to create mechanical leverage.
Evaluation of Design
Analysis
CAM MATLAB
An eccentric cam was chosen as the cam shape to produce a sinusoidal follower motion. The total amplitude of the follower is given by two times the shaft hole offset. The sinusoidal motion of the followers is translated directly to the motion of the fin rods which can be seen in the sinusoidal fin motion. The cams are press fit onto a ⅜″ D-shaft to restrict both axial motion and rotational motion.
Fastener
CAM Torque analysis with motor
(equations only for now)
Inputs
| Symbol | Value |
|---|---|
| $R$ | 1.25 in |
| $e$ | 0.40 in |
| $s = 2e$ | 0.80 in |
| $n$ | 60 RPM |
| $\omega = 2\pi n/60$ | 6.28 rad/s |
| $N_\text{cam}$ | 8 |
| $\Delta\phi$ | 90° |
| $m$ | 0.084 lbm (38 g) |
| $k$ | 20 lbf/in (3.5 N/mm) |
| $x_0$ | 0.10 in |
| $\mu$ | 0.25 |
| $g$ | 386.09 in/s² |
Kinematics
$$x(\theta) = e(1-\cos\theta)$$
$$v(\theta) = \dot{x} = e\,\omega\sin\theta$$
$$a(\theta) = \ddot{x} = e\,\omega^{2}\cos\theta$$
$$x_{\max} = 2e = 0.80\ \text{in}$$
$$v_{\max} = e\omega = 2.51\ \text{in/s}$$
$$a_{\max} = e\omega^{2} = 15.79\ \text{in/s}^{2}$$
$$\tan\phi(\theta) = \frac{e\sin\theta}{\sqrt{R^{2}-e^{2}\sin^{2}\theta}}$$
$$\tan\phi_{\max} = \frac{e}{\sqrt{R^{2}-e^{2}}} = \frac{0.40}{1.184} = 0.338$$
$$\phi_{\max} = 18.7^{\circ}$$
Force analysis
$$N\cos\phi + mg - F_{s} = m\,a, \qquad F_{s} = k(x_{0}+x)$$
$$N\cos\phi(\theta) = m\,e\,\omega^{2}\cos\theta + k\bigl(x_{0}+e(1-\cos\theta)\bigr) - mg$$
$$N\cos\phi(0) = m\,e\,\omega^{2} + k\,x_{0} - mg \;\ge\; 0$$
$$k\,x_{0} \;\ge\; mg - m\,e\,\omega^{2}$$
$$x_{0,\min} = \frac{mg - m\,e\,\omega^{2}}{k} = \frac{0.084 - 0.0034}{20} = 0.0040\ \text{in}$$
$$N_{\max} = k(x_{0}+2e) - mg - m\,e\,\omega^{2} = 20(0.10+0.80) - 0.084 - 0.003 = 17.9\ \text{lbf}\;(79.6\ \text{N})$$
Drive torque
$$T\,\omega = (N\cos\phi)\,\dot{x}$$
$$T_\text{cam}(\theta) = \bigl[m\,e\,\omega^{2}\cos\theta + k(x_{0}+e(1-\cos\theta)) - mg\bigr]\,e\sin\theta$$
$$T_\text{fric}(\theta) = \mu\,N(\theta)\,(R-e\cos\theta)$$
$$T_\text{cam,peak} \approx 4.8\ \text{lbf}\cdot\text{in}\quad (\theta \approx 120^{\circ})$$
$$\bar{N} \approx \frac{N_\text{min}+N_\text{max}}{2} = \frac{1.9 + 17.9}{2} \approx 10\ \text{lbf}$$
$$\bar{T}_\text{fric} \approx \mu\,\bar{N}\,R = 0.25 \times 10 \times 1.25 \approx 3.1\ \text{lbf}\cdot\text{in}$$
$$T_\text{shaft} \approx 8\,\bar{T}_\text{fric} \approx 25\ \text{lbf}\cdot\text{in}\;(2.8\ \text{N}\cdot\text{m})$$
$$P = T_\text{shaft}\,\omega \approx 18\ \text{W}$$
Future Work
- Two camshafts to allow for steering
- More machined components to allow for higher torque
- Sensors
- Fin rod adaptations or additional tilt motors that allow it to work at different angles (such as pointing straight down for land movement or optimizing movement based on environment)
- Non-PLA hull for better waterproofing
- Fully enclosed hull to allow diving