Licentiate seminar

A Simple Model of the Mechanics of Trombone Playing

Defendant Main Advisor Extra Advisor Date
Gitte Ekdahl Martin Lesser 2001-03-15

Annika Stensson, Fordonsdynamik, KTH

Evaluation committee


To study human motion in general, the motion when playing the trombone has been examined. This makes it possible to work with a simple mechanical model and thus get results that are easier to interpret. Calculations from the model have been compared to measurements from experiments. The arm-trombone system consists of a rod, tilted at a fixed angle, and two bars, connected by a hinge, that represents the arm. The shoulder consists of another hinge and is placed level with the trombone. The hand is allowed to slide without friction along the trombone. The system has only one degree of freedom and the behavior is similar to that of a pendulum. Energy can be added to the system, by applying an impulse in the beginning of a motion. Apart from that, gravity is the only active force. Under these conditions the equations of motion for the system have been calculated. Two subjects took part in the experiment - a professional trombone player and a student. They played three types of musical note sequences: 1) different movements between the seven possible positions, 2) a short musical excerpt, and 3) randomly generated notes. The 3D trajectories of the six measured points (LED), placed on the trombone and the right arm, where recorded by an Optotrak system. The experiments where simultaneously recorded on video. When comparing the models and the subjects motions, the hands displacement along the trombone was chosen as the best suited variable to examine. The agreement turned out to be good, especially for slow motions. The results imply that gravity provides the main force and control mechanism used in trombone playing. Skilled trombonist use less energy than less skilled, which can be assumed to depend on that they have learned to optimize their own force input and take more advantage of the force supplied by gravity. Finally, different ways to expand the present study, are discussed.
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