Biomechanics Background and Initial Specifications
Bryan Carlton1, Aniruddha Anand Damle1, Anson Kwan1, Jacob Yoshitake1
Team 2: Swimming
1Ira A. Fulton Schools of Engineering
I. Bio Inspiration
The organism that we will draw inspiration from for our research question and system are eels. Eels exhibit a form of undulatory motion called anguilliform locomotion which propagates waves along their spines [1]. The five most relevant sources about eels and fish based undulatory motion are as follows:
I. Hydrodynamics of undulatory propulsion [1]* II. Muscles, elastic energy, and the dynamics of body stiffness in swimming eels [2]* III. The hydrodynamics of Eel Swimming [3] IV. The hydrodynamics of eel swimming II. effect of swimming speed [4]* V. Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming [5]
Of these sources, we will discuss I, II, and IV since they are the most relevant to our research question.
Hydrodynamics of undulatory propulsion discusses the history of existing work conducted on different forms of undulating locomotion and propulsion [1]. This is particularly helpful for our research question because it provides context and basis of knowledge as we start to explore anguilliform locomotion. Additionally, from this paper, we are able to extract critical information about the gait cycle and time duration of a single oscillation for eels. Muscles, elastic energy, and the dynamics of body stiffness in swimming eels analyzes the kinematic and dynamic properties of eels to derive generalized values regarding muscle activation, work, and stiffness along the body of eels [2]. This research is pertinent to our research discussion because it gives us information regarding how to link kinematic properties of eels to the foldable system that we are interested in developing. The most relevant values include the weight, length, and body cross sectional area. These values are important to deriving the linear velocity of eels as well as provide a method of comparing these elements of our device against an eel. The hydrodynamics of eel swimming II. Effect of swimming speed discusses the kinematics and hydrodynamics of eels but goes into further detail regarding dynamic conditions that eels swim under [4]. Through the method of using two synchronized high speed cameras, the researchers were able to calculate frequency, wave speed, velocities of the system, and jet speeds produced by the eels [2]. This information is valuable to us because it allows us to approximate the linear velocity of eels as well as the power needed to sustain this form of locomotion. We are then able to specify the requirements needed for a servo motor to power our system.
II. Other bio-inspired robots
Although the team has already decided on an eel inspired design, it is also important to look at other similar designs and other sources of biological sources. Below are five different sources that detail different bio-inspired robots. I. Kinematic Evaluation of a Series of Soft Actuators in Designing and Eel-inspired Robot [6]* II. How the Body Contributes to The Wake in Undulatory Fish Swimming: Flow Fields of a Swimming Eel [7]* III. Thrust generation during Steady Swimming and Acceleration from Rest in Anguilliform Swimmers [8] IV. Development and Motion Control of Biomimetic Underwater Robots: A Survey [9] V. Flow patterns of Larval fish: Undulatory Swimming in the Intermediate Flow Regime [10]* Kinematic Evaluation of a Series of Soft Actuators in Designing and Eel-inspired Robot This paper discusses the motion generated through soft actuators in an eel inspired robot [6]. Despite this being a soft robot, it provides an in depth analysis and data on the locomotion of an eel like robot design. As well this paper provides information on the manufacturing of their actuator which can guide the team’s design. How the Body Contributes to The Wake in Undulatory Fish Swimming: Flow Fields of a Swimming Eel This paper discusses the body mechanics, and how that affects the thrust of the robot [7]. This paper provides the kinematics of an eel like robot. It also provides helpful analysis of the undulatory movement that eels and similar fish use to move through water Flow patterns of Larval fish: Undulatory Swimming in the Intermediate Flow Regime This paper focuses on fish larvae designs, and the forces between the body of the larvae and the water [10]. This paper provides helpful force analysis between water and submerged undulatory robots. Having these force interactions helps the team understand how the water affects movement and stabilization of the robot system.
III. Table
| Parameter | Unit | Value Range | Reference |
| Length | m | .024-.033 | [2] |
| Weight | kg | 0.037-0.057 | [2] |
| Frequency | Hz | 1.3 +/- 0.10 | [4] |
| Wave Speed | L/s | 0.39 +/- 0.02 | [4] |
| Slip | L/L | 0.784 +/-0.002 | [4] |
| Max Area | 𝑚2 | 0.0001018 | [2] |
| Gait Time | s | 0.26 | [1] |
IV. Other Assumptions
Using the data that was found in Table 1, we can now calculate the velocity and energy consumed for anguilliform motion. The slip ratio is defined as the swimming speed of the body (U) over the wave speed (V). 𝑆𝑙𝑖𝑝 = 𝑈 (1) 𝑉 From equation 1, we were able to calculate the body speed to be 0.3058 or . In order to find 𝐿 𝑠 the linear speed, we first had to convert the flow rate to and got a value of 𝑚3 𝑠 3. 058 × 10−4 . Then using the volumetric flow equation: 𝑚3 𝑠 𝑄 = 𝐴 𝑣 (2) where Q is the volumetric flow, A is the cross sectional area, and v is the linear velocity. Using equation 2, we get a linear velocity of 3.003 . 𝑚 𝑠 From this we can now deduce the approximate energy and power used during the gait cycle. Using the kinetic energy formula: 𝐾𝐸 = 1 (3) 2 𝑚𝑣2 Where KE is the kinetic energy, m is the mass, and v is the velocity. We calculated the kinetic energy as 0.213 Joules. With this we can now calculate the approximate power consumption of the gait since we know both the energy and duration of the gait cycle. Using the power equation: 𝑃 = 𝑊 (4) Δ𝑡 where P is power, W is work or energy, and Δ𝑡 is the change in time, we are able to calculate the power of a single gait phase of anguilliform locomotion is 0.819 W.
V. Figures
Figure 1. Four main categories of fish undulatory motion. The top figures denote the phases of a single gait phase and the lower visualize the midline movement of each motion [1].
Figure 2. Flow of water generated from eel motion. Red represents clockwise motion and blue represents counter clockwise flow [3].
VI. Engineering Representation
Figure 3. Engineering representation of proposed system
As seen in Fig 3 the proposed system will consist of twelve rigid links connected through eleven joints which will be acting as the torsional spring in the system. All the links will be represented with their own respective masses so in order to properly model the dynamics of this system, inertias will need to be included for all twelve links. The main actuator for this system will be a servo input on the first link (farthest left on Fig 3). This servo will be run using position control so that we can tune and control the maximum and minimum position of the output shaft.
VII. Discussion
Discuss / defend your rationale for the size animal you selected.
We selected the eel as inspiration for our research question because anguilliform locomotion is one of the few undulatory motions that only requires a singular input for the entire system. Traditional fish locomotion has multiple fins in conjunction with an oscillatory motion. This would require additional pieces and increased complexity in order to create an aquatic robot. By gaining inspiration from eels and understanding how to precisely tune a segmented spine, it is possible to create locomotion through a single motorized actuator. This would greatly reduce the cost and complexity of the system and allow us the flexibility to replicate or draw inspiration from anguilliform locomotion by simply tuning the joint stiffness.
Find a motor and battery that can supply the mechanical power needs obtained above.
From section IV, we calculated that the total power of the gait cycle is 0.819 Watts. Using this and the weight of an eel from Table 1, we calculated a power/weight ratio of 16.38 W/kg. Using this information, we selected two perspective servo motors for our system. The first choice is the SG90 Micro Servo Motor[11] due to its low cost, light weight and relatively high power output. However, it does not appear to be waterproof, so additional measures will need to be taken to ensure that it does not succumb to water damage. On the other end, the WEISE DS3218 Servo Motor[12] is heavier, but has much higher power output and is waterproof. Though it is more expensive and heavier, the waterproofing is much appreciated and the higher torque allows the system more power to operate in the water. We will purchase the SG90 initially, and if the robot needs more torque or there are problems with water damage, the DS3218 will be purchased as a replacement. For a battery, a Blomiky 6V 2200mAh battery[13] will be able to operate either of the servos and meet power requirements. This will be encased in a waterproof housing along with the microcontroller to reduce chance of water damage.