A couple further clarifications... 1. The platform would then receive both rotations and translations, and the Yrot of the sphere would remain independent of both. This is where the math is eliminated. 2. I showed the picture with the platform outside the sphere, hoping to illustrate the "joint" thereby. But in reality, you'd want to locate the platform inside the sphere, with both offsets (green cross) adjusted to be in the middle of the sphere.

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