Three legs, one platform

A 3-RRR planar parallel mechanism at (0.00, 0.00) turned 0.0°, elbows up/up/up. The three actuator angles were computed one leg at a time and independently, which is what makes this direction cheap. The dashed lines extend each leg's second link: those are the three forces the legs can transmit to the platform, and the mechanism is controllable exactly while they stay independent. Here they miss one another by 0.520, and the smallest singular value of the three is 0.9000. At this position the platform can be turned through 206° in all before a leg runs out of reach.