I am designing an animatronic head, which has five degrees of freedom: pitch, roll and yaw for the head part, and pitch and yaw for the neck part. However, the yaw movements for the head and neck are defined to be identical – if the neck rotates 7°, then the head also rotates 7° – so there are actually just four parameters determining the position of the system:
If I do this the "obvious" way, with gimbal arrangements at the two centers of rotation, that poses some practical problems for me in how to construct and drive the thing. It occurs to me that it might be possible to instead build a linkage out of rods connected by ball joints (or similar), such that I can get the same motion by driving the ends of four of the rods along (preferably) linear tracks:
This diagram is only a rough suggestion of the sort of thing I mean (I am thinking of examples like this and this). The idea is that the three pink nodes are attached to the head, the three green nodes are attached to the neck, and the four yellow nodes are independently driven to control the geometry of the whole system. There would also be some number of floating nodes (not shown).
Intuitively, it seems like, with rods of the right length connected in the right topology, it should be possible to make every vector $<A,B,C,D>$ correspond to exactly one value of $<\theta_1,\theta_2,\theta_3,\theta_4>$ over a finite range. As long as there are no problems with singularities or things like that, it would "just" be a question of translating the rotation angles into ABCD values to get any desired motion.
Given the design of the linkage, the problem of converting between the input parameters and the Euler angles is well documented, and I can use a constraint-based solver like SolveSpace to resolve the dimensions. What I don't know is how to design the linkage in the first place.
My problem is that as a non-engineer, I don't know the terms to frame my question. For instance:
- is there a general term for this kind of system (rods connected by notional ball joints)?
- there are some obvious (and perhaps less-obvious) constraints on the topology – is there a name for this subject?