In order to maintain balance and traction, the motion paths and cyclical timings of a wall climber's legs must be fine tuned. The leg's end effector, or foot, must maintain a steady and prolonged contact with the wall. Push in too much and the linkage will stall, push in too little and the foot will slip, so a near linear motion profile is desired. A compliant foot, such as one made of rubber or springs, could allow for more flexibility in the system, but excessive compliance might diminish the foot's traction against the wall. With these challenges in mind, our group has chosen a leg geometry that we believe strikes the balance between contact force and compliance. A sketch of this linkage is shown below.
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LP = 65mm
Offset angle theta = 56°
Foot angle delta = 80°
L1 is the ground link that will be connected statically to the rest of the climber body. L2 is the driving link that will be rotated around the origin point at a constant angular velocity. The ground link is offset by theta = 56° from the X axis so that the outer path of position P is as parallel to the Y axis as possible. To help visualize this motion, an animation of the linkage is shown below.
Figure 5: Animation of the leg linkage and the end effector point P. Dotted arrows represent the velocities at each point.
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A very desirable wall climbing motion can be seen in Figure 5. Point P, represented by a yellow dot, has a near linear path when it's further away from the origin (Pressing up against the wall). The specific foot angle and link lengths needed to obtained obtain this particular motion resulted from multiple stages of analysis. First, we had to confirm the linkage's rotational range and degrees of freedom. Next, we had to observe the end effector's position, velocity, and acceleration profiles, tweaking lengths and angles in order to manipulate different characteristics of the path. Finally, we estimated the pressing force of the legs against the walls, making sure the resulting friction force would overcome the gravitational force on the climber. Each of these analysis stages are presented in the following subsections.
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Using MATLAB, our group was able to illustrate the motion cycle of the end effector P, along with its accompanying velocity and acceleration values. We used this visualization to correct the path's flatness, length, and thickness.
NOTE: For each of the graph's graphs below with theta 2 as their x component, the angle is that of L2 with respect to the global X axis shown in Figure 4, not the ground link.
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