Part 3 – Robotizing Big Ben
Documents allowed. School scientific calculator allowed.
The hour and minute hands of Big Ben in London are 2.6 m and 4.58 m long and have masses of 68.6 kg and 97 kg respectively.
The clockwork is old now and should be replaced by state of the art 21th century technology. We study here the motorization of the minute hand. The selected motor comes from Maxon. It is a 400 W brushless, reference 167131 (see below).
The gearboxes that can be associated with this motor are listed below.
1. Select the adapted gearbox that is compatible with the maximum torque on the hand due only to gravity. This maximum occurs every quarter and three quarter of an hour. Due to the
presence of a counterbalancing mass, the center of mass of the minute hand is located at a distance of only 10 cm from the axis.
2. An EPOS controller actuates the motor. This controller implements a position loop that runs at a sampling frequency of 1 kHz. Il has an interface for an incremental encoder and is able to count with quadrature accuracy. We want to generate a continuous rotational motion for the minute hand. Determine the minimal resolution of the encoder.
3. Finally we choose a step-by-step motion for minute hand, mainly for power efficiency reasons.
Every minute, the hand moves from the last dial increment to the next. Thus, the reference of the position loop is a succession of steps. We need a position accuracy of 10 minutes of arc.
Determine the according minimal resolution of the encoder.
