Joint limits

Joint	Limit	Value (±)	Unit	Why?
Hip	Position	1.26	rad	Geometry: cables fully stretched
Hip	Velocity	28.8	rad/s	Details below
Hip	Torque	16.0	Nm	Peak torque (< 1 s) from the qdd100 spec
Knee	Position	2.51	rad	Geometry: wheels touching hip actuators.
Knee	Velocity	28.8	rad/s	Details below
Knee	Torque	16	Nm	Peak torque (< 1 s) from the qdd100 spec
Wheel	Position	-	-	-
Wheel	Velocity	111	rad/s	Details below
Wheel	Torque	1.7	Nm	Peak torque from the mj5208 spec

Maximum velocity for a qdd100

Peak velocities for the qdd100 are rated as 3,600 dps at 36 V and 2,300 dps at 24 V. Assuming a linear velocity-voltage relationship (which is a big assumption, for instance the actual maximum velocity will also depend on servo.pwm_rate_hz) leads to 1,650 dps at the 18 V of the RYOBI batteries used on Upkie, or equivalently 28.8 rad/s after conversion and rounding.

Maximum velocity for an mj5208

The maximum velocity from the mj5208 spec is 7500 rpm, or approximately 785 rad/s. Multiplying by the wheel radius of your typical Upkie (between 5 and 6 cm), we obtain a ground speed comparable to that of a car on a highway. We scale this down a notch! Backtracking from a top ground speed at 20 km/h, we obtain a maximum velocity around 111 rad/s.