Counterbalanced nudges move the kaleidocycle's center of mass #33

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opened 2025-01-21 20:37:21 +00:00 by Vectornaut · 1 comment

Vectornaut commented

2025-01-21 20:37:21 +00:00

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Consider a kaleidocycle where the hinges have length 1 and the other edges have length \sqrt{5}/2. Arrange it so that three hinges lie in a plane perpendicular to the axis. These hinges connect three "inner vertices," which meet on the axis, to three "outer vertices." When we nudge the inner and outer vertices at the same speed in opposite directions along the axis, we want the kaleidocycle to do a pure twisting motion, with its center of mass stationary.

The tangent space projection used in pull request #29 sends this nudge to a motion that moves the center of mass along the axis, rather than the pure twisting motion that we want. This is demonstrated in examples/kaleidocycle.rs on the kaleidocycle-example branch.

Consider a kaleidocycle where the hinges have length $1$ and the other edges have length $\sqrt{5}/2$. Arrange it so that three hinges lie in a plane perpendicular to the axis. These hinges connect three "inner vertices," which meet on the axis, to three "outer vertices." When we nudge the inner and outer vertices at the same speed in opposite directions along the axis, we want the kaleidocycle to do a pure twisting motion, with its center of mass stationary. The tangent space projection used in pull request #29 sends this nudge to a motion that moves the center of mass along the axis, rather than the pure twisting motion that we want. This is demonstrated in `examples/kaleidocycle.rs` on the [`kaleidocycle-example`](src/branch/kaleidocycle-example) branch.