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The next one is a variable piston stroke mechanism used in automobile engines and uses a linear actuator to move a pivot point along a circular path to modify the stroke of a piston. To change the stroke of the piston, the location of the pivot point on the speed control radius bar is changed along a circular slider. This mechanism requires a difficult to make circular slider and a linear actuator, so it was not chosen.

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After some more research we found a simple variable stroke mechanism well suited to our task that is used in a ratcheting continuously variable transmission(CVT). In this mechanism, the oscillation amplitude of a link connected to a ratchet is adjusted to control speed. By decreasing oscillation amplitude, the link moves over a smaller amount of distance each cycle, thus the output connected to the ratchet rotates a smaller amount per cycle, thus speed is decreased. By using a several of these mechanisms in parallel, one can attain nearly continuous rotation of the output shaft. To change the stroke of the link, one changes the location of the pivot point of the speed control link. This works much the same way as the variable piston stroke mechanism shown above, except that a rotatable link is used instead of a slider. This mechanism is well suited for use in our project because, it is simple, compact, contains no slider joints, and a high mechanical advantage(1:4). This mechanism was selected.

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To get a general idea of the motion of this mechanism, we drew it up in Working Model and simulated it. Immediately a problem was discovered, the mechanism was found to shift not just the amplitude of the output link, but the zero amplitude. The zero amplitude being the location the link oscillates around. This is fine for a mechanism that is in a ratchetting CVT, but not so for a quadruped robot. In a ratchetting CVT all that matters is that the amplitude change, but doing so in a walking robot can cause the walking robot to become unstable.

To get around this, the link lengths and pivot locations were tweaked in Working Model. However doing so in Working Model turned out to be an arduous and time consuming process, so the position equations were derived and a simulation of the linkage was written in Javascript. This allowed us to quickly and easily change linkage parameters and obtain values for linkage amplitude and zero amplitude in real time to optimize the linkage. We then tweaked the parameters until the desired amplitude variation of 20-30 degrees was attained and zero amplitude variation was minimized. In the end we were able to get the required amplitude variation with an input angle range of 38°-80° and with a zero amplitude variation of 1°.

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One can access the linkage simulation here.

Variable Stroke Mechanism Prototype

To validate that the variable stroke mechanism worked we built a prototype out of and FR4 and lexan. We chose to make the links an intend to construct much of our robot out of FR4, a glass reinforced epoxy laminate, because FR4 has a high specific strength and is quite cheap. We used bolts for the joints to enable the prototype to be easily disassembled, but intend to use 1/8" steel shaft with E-clips and washers for the final version. We actuated the input crank with a Polou 50:1 micro-HP motor and used a standard hobby servo control the amplitude. A video of the system is shown below(click on the picture)

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