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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Note: Our leg linkages are ran by two gear trains. A motor is connected to these gear trains by a 3:1 gear ratio. We do not consider this part of the mechanism in our leg force analysis because it does not directly determine the mechanism's ability to climb. More so, it determines how long the legs can operate as the linkages work against internal friction. The weight of the robot and friction at the feet and weight of the robot have a much greater influence over the mechanism's climbing ability. Our gear system is relatively simple and is unrelated to the kinematic motion, so we've left out its analysis.
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