# Robotics applied to sport engineering

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Advanced Robotics, Vol. 14, No. 5, pp. 377 – 379 (2000) Ó
VSP and Robotics Society of Japan 2000.

Robotics applied to sports engineering
KENJI HASEGAWA ¤ , SHIRO SHIMIZU and MASATADA YOSHIZAWAFukui University, 3-9-1 Bunkyo, 910-8507 Fukui, Japan

Keywords: Mathematical model; equation of motion; computer simulation.

We study mathematical models of skiing, snowboarding andhorizontal-bar gymnastics. We assume the players to be muti-joint, muti-link systems represented by stick-pictured gures. The equations of motion for these systems are derived and solved numerically. Controlvariables are a few number of joint angles. The numerical results are put into animations on a computer display.

SKIING

In Fig. 1, we show the behavior of our model skier performing repeated turnson a at slope viewed from the horizontal direction. This model skier can control only the rotation angle Á around the femur at the hip joint. Through this angle, the edging angle µ of the ski iscontrolled. The interaction between the ski and snow surface is assumed to be the frictional force. The unknown variables are µ, the directional angle ! of the ski, the position of the top of the ski x1 andx2 , the resistant force FS of the snow surface against skidding, and the vertical resistant force FB of the snow surface. For these variables, we have the following simultaneous equations, whichhave unique solutions under appropriate initial conditions: R Ak1 µ CAk2 ! CAk3 x1 CAk4 x2 CAk5 FS CAk6 FB D Ak7 ; R R R .k D 1; 2; 3; : : : ; 6/: (1)

Figure 1 was drawn by the solution of theseequations. Figure 2 is Fig. 1 transformed into a wire-frame image equipped with two skis.
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E-mail: rakugi@sec.icpc.fukui-u.ac.jp

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K. Hasegawa et al.

Figure 1. Repeated stable skiing turnsof the present model.

Figure 2. Wire-frame image of the present model of skiing.

Figure 3. Repeated stable snowboarding turns of the present model.

Figure 4. Wire-frame image of the...