9.3.2 The Galluzzo bowing machine

To understand the experimental results shown in section 9.3 and 9.6, it is useful to know a bit about the design and capabilities of the bowing machine used in the studies. The bow motion is provided by a linear motor, which propels a trolley carrying a system that simulates the player’s wrist. A clamp that can hold either a conventional bow or a rosin-coated perspex rod is flexibly mounted, and a vibration shaker provides an actuation force for controlling the bow force. The system can be seen in Fig. 1, in this case with the perspex rod in place. Strain gauge sensors monitor the force applied to the bow clamp. Through a combination of open-loop control, closed-loop feedback compensation and careful hardware design, the bowing machine can change bow acceleration with a response time of around 10 ms while maintaining constant bow force with an accuracy of $\pm3 \%$. Full details of the mechanical design, control strategy and calibration procedure for this rig can be found in [1].

In all the experiments to be described here, this machine was used to bow the D string of a cello. The cello is held in a supporting frame, which approximately mimics how a player would hold the instrument. The cello sits on its endpin as usual, and adjustments to the projecting length of that endpin are used to set the bowing point $\beta$. The body of the cello is supported by padded clamps providing the player’s “knees” and “left hand”. The string to be bowed is aligned to be vertical, perpendicular to the line of the bow, which is pressed against it in a horizontal plane. The arrangement can be seen in Figs. 2 and 3. The bridge of the cello is equipped with a piezoelectric bridge-force sensor, as described in section 9.1.1.

The machine is designed for bow strokes in which the bow is in contact with the string throughout: it cannot do “bouncing bow” strokes. But within that family of bow gestures, the machine can equal or exceed the capabilities of a human. For the experiments to be described here, two types of bowing gesture were used.

For the Schelleng diagram tests, the bow speed was set to the constant value 0.05 m/s, and a carefully-tailored initial bowing gesture was used to establish Helmholtz motion prior to each measurement. The force and speed were then adjusted smoothly to the desired values, and these were sustained for two seconds. Bridge force was measured for 0.1 s at the end of that time, and used to classify the string’s motion. Changes in the value of $\beta$ were made by hand, so each column of the Schelleng diagram was measured as a separate run.

The Guettler diagram tests, to be described in section 9.6, were more straightforward. The required gesture in each case involved a constant bow force, and a bow speed starting from rest and then growing with a constant acceleration. The bridge force for the first 0.25 s of the transient response was recorded in each case. The values of force and acceleration were varied to scan the Guettler diagram, and the entire $20 \times 20$ grid of points was run in a single experiment, controlled by the computer.

[1] Paul M. Galluzzo and Jim Woodhouse; “High-performance bowing machine tests of bowed-string transients”, Acta Acustica united with Acustica 100, 139–153 (2014)