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A self-balancing electric unicycle consists of a frame+pedals that the rider stands on, a motor where the stator is attached to the frame+pedals, and a rotor which is attached to the wheel+tire.
An EUC is similar to an inverted pendulum: the EUC frame is free to rotate about its axis, limited by motor torque. EUC plus rider is similar to a double inverted pendulum, with the rider free to rotate relative to EUC frame, limited by frame|rider torque. Any torque exerted by the motor onto the EUC frame has to be countered by an opposing torque from the rider to end up with zero net torque on the EUC frame so that the EUC frame does not rotate.
The pedals are long enough (8 to 10 inches or so front to back) for a rider to be able to generate or experience adequate torque with the frame. There may also be other contact points for the rider to be able to generate or experience a torque with the frame. To simplify this question, assume that only the pedals are being used (some riders actually ride this way). Self-balancing components and algorithm will make corrections as needed to keep a leaned rider balanced, holding the rider's lean angle steady and preventing rider from falling forwards or backwards.
Assumptions: During constant acceleration with zero net torque on the frame, the motor is exerting a forwards torque onto the wheel+tire, coexistent with the motor exerting an equal in magnitude backwards torque onto the frame+pedals. Splitting this up into Newton third law like pairs, the forwards torque exerted by the motor onto the wheel coexists with a backwards torque exerted by the wheel onto the motor. The backwards torque exerted by the motor onto the frame coexists with a forwards torque exerted by the frame onto the motor. The backwards torque exerted by the frame onto the rider coexists with a forwards torque exerted by the rider onto the frame.
Leaning related to linear acceleration: The rider has to lean forwards in order to be balanced due to the forward force exerted by the pedals related to linear acceleration.
Question 1: Does the rider need to be further leaned forwards due to the backwards torque exerted by frame onto rider which coexists with a forwards torque exerted by rider onto frame?
Question 2: Assuming the rider does need to lean further forwards, and assuming zero net torque on the frame, is the forwards torque the rider exerts onto the frame exactly equal to the forwards torque that the motor exerts onto the wheel+tire?
An EUC is similar to an inverted pendulum: the EUC frame is free to rotate about its axis, limited by motor torque. EUC plus rider is similar to a double inverted pendulum, with the rider free to rotate relative to EUC frame, limited by frame|rider torque. Any torque exerted by the motor onto the EUC frame has to be countered by an opposing torque from the rider to end up with zero net torque on the EUC frame so that the EUC frame does not rotate.
The pedals are long enough (8 to 10 inches or so front to back) for a rider to be able to generate or experience adequate torque with the frame. There may also be other contact points for the rider to be able to generate or experience a torque with the frame. To simplify this question, assume that only the pedals are being used (some riders actually ride this way). Self-balancing components and algorithm will make corrections as needed to keep a leaned rider balanced, holding the rider's lean angle steady and preventing rider from falling forwards or backwards.
Assumptions: During constant acceleration with zero net torque on the frame, the motor is exerting a forwards torque onto the wheel+tire, coexistent with the motor exerting an equal in magnitude backwards torque onto the frame+pedals. Splitting this up into Newton third law like pairs, the forwards torque exerted by the motor onto the wheel coexists with a backwards torque exerted by the wheel onto the motor. The backwards torque exerted by the motor onto the frame coexists with a forwards torque exerted by the frame onto the motor. The backwards torque exerted by the frame onto the rider coexists with a forwards torque exerted by the rider onto the frame.
Leaning related to linear acceleration: The rider has to lean forwards in order to be balanced due to the forward force exerted by the pedals related to linear acceleration.
Question 1: Does the rider need to be further leaned forwards due to the backwards torque exerted by frame onto rider which coexists with a forwards torque exerted by rider onto frame?
Question 2: Assuming the rider does need to lean further forwards, and assuming zero net torque on the frame, is the forwards torque the rider exerts onto the frame exactly equal to the forwards torque that the motor exerts onto the wheel+tire?