A simple model of the mechanics of trombone playing

Sammanfattning: To study human motion in general, the motion when playingthe trombone has been examined. This makes it possible to workwith a simple mechanical model and thus get results that areeasier to interpret. Calculations from the model have beencompared to measurements from experiments.The arm-trombone system consists of a rod, tilted at a…xed angle, and two bars, connected by a hinge, thatrepresents the arm. The shoulder consists of another hinge andis placed level with the trombone. The hand is allowed to slidewithout friction along the trombone. The system has only onedegree of freedom and the behavior is similar to that of apendulum. Energy can be added to the system, by applying animpulse in the beginning of a motion. Apart from that, gravityis the only active force. Under these conditions the equationsof motion for the system have been calculated.Two subjects took part in the experiment–aprofessional trombone player and a student. They played threetypes of musical note sequences: 1) di¤erent movementsbetween the seven possible positions, 2) a short musicalexcerpt, and 3) randomly generated notes. The 3D trajectoriesof the six measured points (LED), placed on the trombone andthe right arm, where recorded by an Optotrak system. Theexperiments where simultaneously recorded on video.When comparing the models and the subjects motions, thehands displacement along the trombone was chosen as the bestsuited variable to examine. The agreement turned out to begood, especially for slow motions.The results imply that gravity provides the main force andcontrol mechanism used in trombone playing. Skilled trombonistuse less energy than less skilled, which can be assumed todepend on that they have learned to optimize their own forceinput and take more advantage of the force supplied bygravity.Finally, di¤erent ways to expand the present study, arediscussed.