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The use of a nitinol actuator for the mechanisms driving input prevents the use of conventional circular crank inputs common to walking mechanisms. The desired input shape from a nitinol actuator is an elliptical shape. This shape is necessary because it offers opposing working faces that allow the nitinol spring and return spring to pull a follower pin along. Figure 1 below shows a representation of the input shape provided by a nitinol actuator.
Figure 1.
Representative input shape
Like conventional walking mechanisms, a nearly perfectly flat position profile along the bottom is ideal however there are some extra considerations. Making a walking mechanism for lunar applications also warrants a design that has a large step height. This is primarily needed for obstacle avoidance on uneven or rocky terrain to prevent the foot from getting caught on terrain during its return motion. The figure below shows an example of an acceptable output position profile. Notice how the bottom of the profile is flat and the return path above has a large clearance height.
Figure 2.
Ideal foot output position profile
Due to shipping delays, the actual output from the nitinol actuator has not been determined yet. In order to make progress with analysis, a slider crank mechanism was designed to generate an elliptical shape to stand in for the nitinol actuator. The output of this mechanism was then coupled to the input of a modified Klann walking mechanism. Figure 3, below, shows the first iteration of the walking mechanism with the slider crank ellipsoid generator as the input.
Figure 3.
First iteration walking mechanism design
Mobility analysis of this mechanism shows there are 7 linkages, 8 joints, 1 half joint, and 1 grounding. Using equation 1 yields that this system has 1 degree of freedom
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Initial motion analysis of the first iteration design meets the design goals fairly well but still has room for improvement. In figure 4, the output position profile at the bottom demonstrates that the mechanism has a relatively high step distance. However it should also be noted that the output motion is not very flat along the bottom. While the bottom section is generally oriented horizontally, there is a significant curve to it that will need to be removed.
Figure 4.
First iteration mechanism and position profiles
In the second design iteration, shown below in FIgure 5, the mechanism’s geometry was altered to create a flatter base profile while maintaining a sufficient change in height from when the foot is in contact with the ground to when it is not. However, one issue with this motion profile comes from the rate at which the foot lifts off the ground; this could present a risk for the mechanism while it is traversing a rocky surface. Ideally, the max height of the foot would occur towards the middle of the base profile. Although the main issue of a non-flat base profile was removed with this profile, it is not evident that the pros of this profile outweigh the cons.
Figure 5.
Second iteration mechanism and position profiles
Position Profile:
In figure 6, the positional set of each joint is mapped to their corresponding x and y position. It can be seen when comparing to the first design iteration, that the only notable change is in Point C and the foot tip. As mentioned above, the positional profile of the foot tip matches more closely with the desired profile; however, to change the foot tip’s profile, the position of point C, located at the obtuse angle of the leftmost ternary link, and the position of point E had to be altered, as the position of the foot tip corresponds with these two positions. Since point E’s profile can only change in magnitude and size, but cannot change geometry, as it is linked to the ground, the main difference comes from Point C, and this is evident when contrasting it to the previous position profile.
Figure 6.
Position profiles of joints
Velocity Profile:
Analyzing the velocity of the foot point as a function of the crank input angle yields the graph in figure 7. It was determined that the foot contacts the ground for input angles between ~1.0 radians and ~2.7 radians. The velocity profile shows that the foot is moving at approximately 1.4 units / sec at the beginning of ground contact and slows down to a minimum of around 0.5 units / sec mid stroke before speeding up to around 5.5 units / sec by the end of ground contact. The return stroke then starts with a high velocity back to the beginning. It should be noted that figure 7 was simulated using a 1 rad/s input angular velocity, and as such different input speeds will change the output speed.
Figure 7.
Foot velocity plot
This velocity profile is not ideal since the velocity during ground contact is not relatively constant. This would lead to an inconsistent movement of a vehicle using a walking mechanism of this design.
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Figure 8 shows a plot of the mechanical advantage at the foot over the entire range of motion of the mechanism. As stated previously the foot contacts the ground for input angles between ~1.0 radians and ~2.7 radians. The plot shows that just as the foot contacts the ground, the mechanism is approaching a high mechanical advantage for the ground stroke. The mechanical advantage decreases and becomes its minimum value just as the ground stroke is ending and the return stroke is starting. This is ideal since the return stroke does not experience high loading forces so it is okay for the mechanism to have a low mechanical advantage in this condition. Similarly during the groundstroke, the mechanism has relatively higher mechanical advantage allowing it to operate more easily when the mechanism is loaded with the weight of the vehicle. The second peak in the plot around 4 radians does not matter since the mechanism is still in the return stroke and there is negligible loading. This means that the higher mechanical advantage in this region does not benefit nor disadvantage the mechanism in any way.
Figure 8.
Mechanical advantage plot
Physical Prototype:
Figure 9.
Prototype Mechanism
The Prototype currently consists of the major links and joints for the walking motion based on the Klann Linkage. The Klann linkage was chosen over the Jansen linkage due to the reduced small range of motion for the joints, which better lends itself to compliant mechanisms. The prototype is composed of rigid links with swappable compliant rolling contacts (CRCs). The joints were chosen to be swappable as breakage in the joints was a known risk factor.
Figure 10.
Initial prototype joint:
The initial prototype joints had a flexible strip that allowed for motion. The anisotropic properties of 3D printing were taken into account by printing the strips flat on the plate as opposed to vertically, allowing them to be more flexible.
Figure 11.
Used flexible strip in initial prototype joint:
Unfortunately, the initial flexural elements had issues that rendered them inoperable. The strips had unreliable bend radii, often creasing sharply and breaking. In addition, the force of the joint varied across its range of motion, resulting in changes in the force profile due to resistance in the flexural elements.
Figure 12.
Initial compliant rolling contact:
Pictured above is the initial attempt at creating a compliant rolling contact, or CRC. These CRCs have the special property of having mostly constant forces across its range of motion. In addition, they have predictable bend radii, providing repeatable motion despite (reasonable) external loads. The initial iterations had issues with manufacturing, as CRCs are traditionally designed for laser cutting from isotropic materials with relatively low young’s modulus (very flexible). 3D prints, by contrast, often fatigue and fail when bent, breaking from stress concentrators such as line starts, line ends, and between layers.
Figure 13.
Refined rolling contacts
Future iterations took a 3D printing-centric approach to the design of the rolling contacts. The flexural strips were re-designed so that the stress concentrators were located after the attachment points, meaning that they saw minimal loads. Refinements in the printing settings, layer orientations, speeds, temps, and heights, all helped to develop a more flexible, resilient strip. Lastly, for the sake of space efficiency, the bend radii was reduced, and new attachment methods were concocted to better reach the performance of typical laser-cut CRCs.
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