That's a very interesting problem!
I think it could be done with transmitting and receiving transducers on a belt. An ultrasonic pulse, generated by an MCU, which resets a timer, is transmitted. An MCU with receiving and transmitting transducers, on, say, the right wrist, detects the pulse, and immediately retransmits it. The belt MCU detects the retransmitted pulse, and stops the timer. From the speed of sound, and the time for the outward and return journey, the total distance can be calculated. Halving the distance gives the distance from the wrist to the waist.
The distances are relatively small, so enough signal should be present, even if the transmitter and receiver are not line-of-sight. Amplification will be needed for reception.
I'll leave you to work out the details for all four wrists and ankles. :) Some form of encoding will be needed so that the four remote units can be distinguished from each other.
A Google search for similar techniques turned up this, which uses a passive reflector on the hand, with the transmitter and receiver on a microphone stand. I can't see that simpler technique working for Glen's application.