Over the years, I've seen a lot of automata and videos of automata and a thought has been slowly forming about what makes a piece interesting and engaging. And it comes down to speed.
To my eye, an automaton engages the viewer when the movement seems natural, and a lot of the appearance of naturalness depends upon timing. Imagine we're looking at an automaton with a couple of kids on a seesaw. The cycle time of this piece is 10 seconds - it takes five seconds for one end to rise, five more to go back down. Visualize that by moving your hands up and down and counting five seconds up, five down.
Yawn. Have you ever seen a couple of kids go at that pace? Picture it in your mind and figure how long you think real pair of kids would take - 3 seconds for calm kids, 1 for hyperactive kids?
How can we control this? Thinking out loud here, you'd have to work from the final movement backwards, looking at cam profiles, lever ratios, gear train ratios, input (crank/motor) speed, adjusting all accordingly. It's a complicated chain of actions, but if the design doesn't take the end movement speed into account, it can end up looking like the whole mechanism has been soaking in syrup when it operates.
Oddly, I can't recall seeing an automaton that seemed unrealistic because the movements were exageratedly too fast.
What are your processes for getting realistic movement speeds in your pieces? Do you work backwards as above, forwards from the desired crank or motor speed, or set the two end speeds and make the middle bits fit?