Description of the robot
The arm used in the experiments is a direct drive planar chain with two revolute joints and two links, the second of which -the forearm- is very flexible. The first link (the rigid one) is 300 mm long; it has been obtained from an aluminum pipe of 100 mm diameter and 5 mm thickness. The second link has been designed to be very flexible in a plane orthogonal to the two motors axes (the horizontal plane) and stiff in the other directions and torsionally.
It is composed of two parallel sheets of harmonic steel coupled by nine equispaced aluminum frames, which prevent torsional deformations. Each sheet is 700x70x1 mm. The frames are square, 70×70 mm, with a circular hole drilled at the center to reduce their weight. They have a sandwich structure: two external layers of 2 mm thick aluminum enclose an internal layer of 1 mm neoprene. The external layers continuity is interrupted on the opposite sides by four parallel 1 mm cuts, which preserve the neoprene continuity. Being the neoprene very flexible, two parallel hinges are obtained so that the steel sheets are free to bend only in the horizontal plane.
The total mass of the flexible link is about 2 kg. The inertia of the first and second links are respectively J1=0.447 Kg m^2 and J2=0.303 Kg m^2. The motors driving the two links can provide a maximum torque respectively of 3.5 Nm and 1.8 Nm and are supplied by two 20 KHz PWM amplifiers. Each motor is equipped with a 5000 pulses/turn encoder and a D.C. tachometer.
The second link deformations are measured by an optical sensor with a precision of about 0.1 degrees. The light of three lamps positioned along the link is reflected by three rotating mirrors on three detectors. When a detector is illuminated, the position of the corresponding mirror is measured by an encoder. In this way it is possible to know the lamps displacements during the experiments and to reconstruct the link shape with a good approximation.
The electronics used to control the arm has been purposely built and provides the functional interface between the arm sensors and actuators and the control computer, a 33MHz 486DX equipped by a Burr-Brown PCI-20001 parallel communication board. To address a particular device (actuator or sensor) the computer outputs his address on 5 of the available 32 lines and then sends or receives the required values on other 16 lines. Part of the remaining bits are used for the housekeeping of the electronics (reset, status, etc.).
The blocks concerning the motors, the tachometers and the encoders are rather conventional. They mainly consists in the necessary converters and counters and the related electronics. The displacement sensor logic contains a speed regulator for the motor driving the mirrors and a phase locked loop which increases by a factor of 16 the number of the pulses provided by the encoder (a 500 pulses/turn unit). The deflections measured by this sensor are rather noisy and require some processing to improve their quality.