1

ME112 Hippogriff Final Report

Team Bratwürst, Winter Quarter 2012 Mark “Leko” Murphy Steven “Colin” Roach Andrew Whitmore Stephanie Tomasetta

2

Executive Summary Oh no! Baby hippogriffs are running loose on the rooftops of London! In the design challenge “Baby got Beak”, we were tasked as a team of muggle-minded engineers to design a fleet of mechanical hippogriffs to cover up this magical outbreak in the muggle community. To achieve a successful design our hippogriff needed to have the shape of a baby hippogriff, be able to flap its wings, walk on both flat surfaces and at a ten degree incline, have the speed of a real hippogriff and be cheap enough to be easily and quickly mass produced. Our project began with an in depth analysis of various linkages and their corresponding coupler curves. We ran matlab and solidworks simulations and power analysis to determine the most efficient, effective linkage for walking. Paired with this technical, mechanical analysis, we studied the biomechanics of horses (who have a very similar gait to hippogriffs) to achieve an accurate representation of how a hippogriff would walk. We quickly determined that, both for stability and for the appearance of a walking hippogriff, we wanted our design to have three legs on the ground at all times. In addition, we wanted our coupler curve to have a flat bottom, with the least amount of torque necessary from the motor on the bottom flat surface, when the leg would actually be supporting the weight of the body and driving the hippogriff forward. We found that a modified Hoeken’s linkage satisfied all of these requirements, and was therefore the linkage type we decided to include in our final design. The wings were a simple matter of connecting a cam to a rotating shaft, which pushed our wings up and down at a natural frequency. With this analysis in hand we moved on to prototyping. Prototyping presented a number of structural problems previously unforeseen by our matlab simulations. Main issues included the legs slipping, joint connections either locking up or loosening, the hippogriff falling back when attempting to climb the incline and general instability in the legs. Our mechanism had a beautiful coupler curve, but stuck out relatively far from the body and required several connections. This magnified the imperfections in each of the joints. In the end, the vast majority of these issues were fixed simply by making the joints more stable and robust, and shifting the weight distribution within the body. We constructed our final design using masonite for the body panels, brass sleeves for the rotating joints, brass rods for our axles and wooden dowel for structural purposes. Our final motor choice (driven by our power analysis) had a 30:1 gear ratio and operated at 12V. We used a chain and sprocket set from Vex robotics.

Preliminary Leg Design Research The most difficult obstacle to overcome in designing a walking robot is developing an effective walking gait with multiple bar linkages. Because we aimed to make our Hippogriff gait resemble a horse’s, with 3 feet on the ground at all times, we experimented with various 4-bar linkages1 in an attempt to obtain a coupler curve with a flat bottom and a time ratio of ⅓. This experimenting proved to be somewhat successful, although we found that we would need to alter the input crank rotational velocity to achieve a time ratio of ⅓. We originally thought that this would be too complicated to perfect given the time constraints of the project.

1 http://www.mekanizmalar.com/fourbar01.html

3

After extensive research of walking robots, we discovered that Hoeken’s linkage would exactly fit our goals.2 Hoeken’s linkage is a 4-bar linkage that is used to approximate a straight line (see figure 1). However, the 4-bar version produces a problematic coupler curve, that is the flat part of the curve is above the mechanism (which may be useful if we were building a sloth). By modifying the 4-bar version of Hoeken’s linkage to a 6-bar version, we can translate the curve into useful motion. This coupler curve can be seen in figure 2 of the next section.

Figure 1. 4-bar Hoeken's Linkage. Image courtesy of Indian Institute of Technology Bombay

Matlab Leg Simulations Simulations in Matlab allowed us to find out many characteristics about our chosen leg design, including power required for propulsion, overall ground speed and the path of the hippogriff’s foot. Modifying the starter code for a 4-bar linkage given in class, we were able to add 2 linkages to form the required 6 bar Hoeken’s Mechanism. We then brought down the coupler point sufficiently below the mechanism to simulate motion along the ground. After storing the position of this point at equal time intervals, we were then able to construct a velocity curve and calculate power requirements for our motor.

2 Anirban, Guha, and Amarnath C. Adjustable Mechanism for Walking Robots with Minimum Number of Actuators. Mumbai: Indian Institute of Technology Bombay, 2011. www.cjmenet.com.

4

Power and Speed Analysis Although the path along the ground appears to be a straight line in figure 2, taking a closer look reveals a sinusoidal path through space, as shown in figure 3. To find the maximum power required from the motor when driving the Hippogriff along a flat surface, we used the greatest downward y-velocity along this section of the curve (which is when the foot would be in contact with the ground) and multiplied this times the force of gravity for the robot, estimating a mass of 1kg.

Figure 3. close up of coupler curve along ground

Using the required speed of 1 meter in 15 seconds and a crank length of 0.5 inches, the max y-velocity of the foot on the ground is 0.00108 m/s or 0.0424 in/s. Flat Ground:

Intuitively, a Hippogriff walking up the 10º slope demands more power from the motor. To validate this and to calculate the increased power requirement, we simply found the y-component of velocity again, multiplied times the weight of the robot. This time, because of the slope, we had to take into account the x component of the velocity also. 10º Incline:

where Vy and Vx are vectors containing velocities at each point along the ground. max() is a function which returns the maximum value of the resulting vector.3 The shape of our translated coupler curve is ideal for our application for many reasons. The dots on the coupler curve in figure 2 are taken at equal time intervals. As the spacing of the 3 see matlab code in appendix

Figure 2. Units in Inches

5

dots show, most of the time is spent on the ground. This slower motion gives us a mechanical advantage and requires very little power from our motor, as seen in the above calculations. The relatively flat section represents smooth motion along the ground and is kept very close to a constant speed. A constant speed while on the ground is important since 2 other legs are on the ground also at any given time. Our mechanism is a quick release motion as well, which can be easily seen in the figures above. In the fast motion at the top of the curve is where most of the torque would be required. Because this is the section is traversed in while the foot is off the ground, little motor torque is needed.

Results From Simulations with Multiple Legs

Step 1. Back right leg up

Step 2. Front right leg up

Step 3. Back left leg up

Step 4. Front left leg up

Figure 4. Hippogriff Gait

Our goal for the gait of the hippogriff was to have 3 legs on ground at all times. This was motivated both by a desire for stability, as well as by a desire to closely resemble a hippogriff’s walking gait, in which the hippogriff always has three legs on the ground. Through studying a horse’s gait (very similar to a hippogriff’s gait), we realized that not only do horses have three legs on the ground at a time, but the three legs are constantly forming a tripod, a very stable stance. To achieve this we needed to do two things. We needed the legs to spend three times as long on the ground as in the air (have a return time of 1/3), and the legs needed to be synched with one another to produce the continuous tripod stance. The 1/3 return ratio was taken care of by our Hoeken’s linkage design, and through a series of Solidworks simulations

6

we were able to find crank orientations that yielded a gait almost identical to that of a horse’s. In this crank orientation, legs located on the same axle were 180º out of phase with one another, and the two axles (front and back) were offset by 90º.

Body Integration

Figure 5. CAD model front view

Figure 6. CAD model top view

7

We aimed to make our body design as simple and elegant as possible. For the basic framework of the structure, we placed four body panels in parallel. This gave us the basic shape of a hippogriff as well as a solid, yet light, structure to mount all of our components. The panels were connected by wooden dowel. The motor was mounted in the center two panels, slightly behind the center of the hippogriff. Two axles were used to drive the front and back legs. These were connected to the motor using our Vex chain and sprocket set. The front axle was connected to a third axle located at the shoulder of the hippogriff by another chain and sprocket. This axle was used to spin a cam, which rotated our wings up and down. We constructed our final design using masonite for the body panels, brass sleeves for the rotating joints, brass rods for our axles and wooden dowel for structural purposes. Our final motor choice (driven by our power analysis) had a 30:1 gear ratio and operated at 12V. We used a chain and sprocket set from Vex robotics. To aid in the assembly of our Hippogriff, we made extensive use of SolidWorks to outline every mechanism and body connection. This was especially pertinent when assembling our complex leg linkages. Our 6-bar Hoeken’s linkage would have major issues with clearances, as we immediately discovered during our first prototype assembly. We used a section layout for our Hippogriff. Rather than using a horizontal piece to connect the sides of the hippogriff and to mount the motor, we decided to use dowel rods as the connection structures.

Results from Testing The motion of the gait was nearly perfect in our prototypes and matched closely to the tripod formation we found in a horse’s gait. It even sounded very similar to a horse’s walk on hard surfaces. While the gait was on track in testing, it was not very consistent and often would cause the hippogriff’s drive chain to skip because of the leg assemblies getting locked up somehow. These main issues with our initial prototype were mostly due to poor construction of the leg linkages, which we solved in a variety of ways. Our hippogriff was also initially suffering from slipping. We attempted to alleviate this problem by gluing strips of rubber band to the bottoms of the feet. However, this caused extreme problems because our hippogriff feet were in fact scraping the ground on the return cycle. Consequently, the rubber would catch and cause the hippogriff to suffer from spasms. Instead, we glued an extra ⅛” piece of a foot to widen the area of foot.

Another unanticipated issue was from our fasteners and joints. The fasteners would screw tight or unscrew in our first prototype, which caused the linkages to lock up or

Figure 7. Leg Assembly

8

loosen while walking. Loose joints caused major problems because it made the leg assembly very unstable. The loose leg assemblies would drag even during the return phase of the coupler curve or the leg would run into itself, locking up. To overcome this issue, we glued the fasteners shut so that they would not be able to lock up or loosen. Also, by carefully making each leg assembly so there was little room for movement out of the plane of motion we ensured that each leg would be stable and sturdy enough to maintain smooth linkage movement. Another addition to our leg assemblies was the washers glued to the face of one of the links, which you can see in figure 7. The front leg kept getting caught on the fastener at the bottom of the connecting link in our prototype, which was disrupting the movement of the legs and locking up the linkage. These washers were glued to front of the link so that the spacing provided at the top fastener was maintained along the whole link to make up for any bending or angle in the front leg piece. While these changes made for great walking on flat surfaces, the incline walk proved to be more difficult. The main problem came from the weight distribution on our hippogriff. In the initial prototypes the majority of the weight, which came from the 8 AA batteries needed to power our motor, was too far back. With the weight at the back of the robot, whenever the back leg raised the robot would fall back on it and not allow any forward movement. It essentially would lock up the linkages because it stopped the back legs from completing their coupler curves. We redistributed the weight to the front of the hippogriff by moving one of the battery packs to fit between the neck and head Masonite pieces. We also moved the second battery pack a little bit off center underneath the body of the hippogriff to balance out the off centered placement and weight of the motor. Making these adjustments established a balance of weight that allowed the hippogriff robot to smoothly walk on flat surfaces as well as up the incline. Once we had cleared these issues up, our prior analysis and matlab simulations held up and we were left with a very successful design and aesthetic.

Conclusions and Reflections Overall, Team Bratwurst was very pleased with the hippogriff’s performance on testing day. The hippogriff was able to march 1 meter in just over 12 seconds, well below the 15-second speed requirement. It also robustly climbed up the 10 degree incline without any complications. The wings performed beautifully with our simple cam system and the feathers added nice movement and realism to the wings. The gait, stylish wings, and form of the body’s Masonite pieces created the appearance of a real hippogriff, while remaining within size constraints. Our simple design was elegant and utilized very little material, which kept costs low. Figure 8. Skip, Team Bratwurst's Final Hippogriff Robot

9

In future designs, we could increase the gait’s realism by creating legs that had joints that moved with each step. Similarly, we could improve walking performance by finding a coupler curve that had a higher return elevation to ensure less sliding and ease in climbing, which could be found through further optimization in Matlab. We could also incorporate a more robust chain and sprocket to reduce skipping. Overall, however, we were very pleased with the outcome of our efforts.