Determining Height of Platform on Fulcrum Consider this scenario:
We have a platform resting on a fulcrum.
The platform's tilt is controlled by a motor attached to 2 levers:

Is the link between the height of the top of the lever (connected to the platform) and the degree of the motor constant?
I'm struggling to visualise it. I would say that it probably isn't - I imagine as the lower lever becomes vertical, the platform motion decelerates.
How would the velocity of the motor need to change to keep a constant velocity of the platform?
How could we determine the degree of the motor, based on the desired height of the  platform (where the top lever connects).
Forgive me if this seems basic - As usual, I've completely over-complicated this in mind to the point that I just can't concentrate on it anymore.
 A: The ideal coordinates for this sort of problem would probably be these two red-dashed axes corresponding to the two actually-fixed points in your system.

From this perspective, the center of the circle is at $(0, 0)$, the center of the ramp is at a point $(D, 0)$, the point circled describes a simple position $(a \cos \theta, a \sin\theta)$ at a distance $a$ from the center, and the point that we're tracking is at a point $(u, v) = (D + c \cos\phi, c\sin\phi)$ which must satisfy the fixed-distance relation: $$(D + c \cos\phi - a \cos\theta)^2 + (c \sin\phi - a \sin\theta)^2 = b^2.$$
Expanding we can possibly simplify this to:$$ D (a\cos\theta - c\cos\phi) + a c (\cos\phi\cos\theta + \sin\phi\sin\theta) = \frac12 \big(a^2 + c^2 + D^2 - b^2\big).$$
Call the term on the right $Q,$ and define $w = c\cos\phi,$ then isolating $\sin\phi$ gives:$$ac \sin\phi\sin\theta = Q - D (a \cos\theta - w) - w ~a \cos\theta,$$ and squaring this and using $\sin^2\phi = 1 - \cos^2\phi$ gives:
$$(a^2 \sin^2\theta) ~ (c^2 - w^2) = \big(Q - D (a \cos\theta - w) - w ~a \cos\theta\big)^2$$This is then a parabola in $w$ and can be solved by the quadratic formula. There are two solutions, which is indeed a property of the original problem (there are two places $(x,y)$ could be to satisfy those constraints) and it would be interesting to know whether the trajectories of those solutions overlap -- if they do, then the system can potentially "cross over" to the other family of solutions.
You were interested in the height $h$ of the ramp above the ground; this is going to be based on this point $(u,v) = (D + w, \sqrt{c^2 - w^2})$ that I mentioned above.
In any case, there is obviously no linear relationship between $\theta$ and $h$ because, except for this possibility of maybe transferring between two different "tracks", $\theta$ is $2\pi$-periodic while $h$ is not. In other words, if you mount this whole setup astride a canyon, so that the wheel can rotate the whole way, the height must come back to where it started. That is totally impossible if the relationship were a simple linear increase. It also points to the idea that these functions $w(\theta)$ and $h(\theta)$ probably have some interesting Fourier series expansions that make thinking about them much easier.
But of course, for very small angles we can expect that everything here is differentiable and so the results will be approximately linear for small angles with some relationship.
