Download A serpentine robot designed for efficient

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φ2 = tan −1
tan φ1
cos θ
(1)
Note that when θ = 0, the equation reduces to φ2 = φ1. Physically, this means that
when there is no bend in the joint, the input and output shafts move with same
velocity. As the joint angle varies, however, the output shaft undergoes periodic
velocity fluctuations even when input velocity is constant. Computer simulation
shows the degree of speed variation that can be found in the segments of the robotic
snake for even moderate joint angles. The graphic shown in figure 7 was used as the
input to ProEngineer’s motion analysis software. This figure represents a snake seven
segments long with each segment bending at an angle of 25 degrees.
Figure 7: U-Joint Test Setup
For our analysis, a constant angular velocity (180 rad/sec) was applied to the first cam
in the assembly, and the angular velocity of each downstream cam was plotted over
time. The results, plotted in figure 8, demonstrate the severity of velocity distortion
seen in downstream cams. As expected, cam one rotates at the same speed as the
servo motor, while each successive cam rotates with a more distorted motion than the