Robot Models for Skiing and Snowboarding

Shiro Shimizu (University of Fukui)

Introduction

In order to develop both a skiing robot and a snowboarding robot that can model, how a skier on skis and a snowboarder on a snowboard perform turns, it is necessary to understand the basic mechanisms of skiing and snowboarding. Moreover, successful development of such models can have applications in the teaching and learning of skiing and snowboarding. Yet it must be noted that the motions of a skier and that of a snowboarder are complex, thus requiring effective modeling so as to get to the principles. Despite this problematic complexity, I have been able to develop skiing robots and snowboarding robots that now are at least capable to perform turns by means of simple and clear motions. The skiing robots that I have constructed are of the following types: (1) carving- turn models, in which skier ride on the skis along an effective side curve; (2) skidding-turn models; (3) femur-rotation models around its longitudinal axis (performing different postures); and (4) combined models with femur rotation around femur its axes. The snowboarding robots are of the following types: (1) a model with outriggers for repeated and automatic carving turns; (2) a model with outriggers for repeated and automatic skidding turns; (3) a proto-type model; (4) a model with flexion (dorsi-flexion) and extension (plantar-flexion) of the ankles; (5) a model with flexion and extension of the knees; and (6) a model with flexion and extension of the hips.

The structural shape and key features of the skiing models and the snowboarding models

Although the turn models of skiing robots and snowboarding robots were developed in order to attain specific motions for the purpose of this study, as a whole, the skiing robot's structural figure and key features are detailed in Fig.. 1. That of the snowboarding robots are shown in Fig. 2.


Fig. 1 Structure figure (The system) and feature of the skiing models

Fig. 2 Structure figure and feature of the snowboarding models

Results of this study

1. It was shown clearly that the model of femur rotation in the hip joint achieved change of ski posture conforming to that of a straight downhill running posture, to that of the snow plow posture and to that of the traverse posture (Fig. 3). Moreover, the snow plow turn (Fig. 4), the stem turn (Fig. 5), and the parallel turn (Fig. 6), which are the basic turn techniques of skiing, have also reproduced turn techniques approaching that of an actual skier - modeling achieved by means of the femur rotation. The relationship between basic postures and basic turn techniques can be explained as the following: (1) from a snow plow posture, if the outside femur of a turn is rotated inside, it can do a snow plow turn; (2) from a traverse posture, when the both femurs are rotated in the same direction (by internally rotating the outside femur and externally rotating the inside femur of a turn), it can do a parallel turn and wedeln; (3) the first half: from a traverse posture, if the outside femur is rotated inside, it can perform a snow plow posture - the second half: from a snow plow posture, if the inside femur is rotated outside, it can perform a traverse posture - thus becoming a stem turn. The model of femur rotation showed clearly that it is the most important of element for the fundamental skiing postures and turn techniques.


	Straight downhill running posture


Snow plow posture		Traverse posture
Fig. 3 Relation of straight downhill running posture, snow plow posture, and traverse posture


Fig.4 Snow plow turn	Fig,5 Stem turn	Fig. 6 Parallel turn

2. The combined model (Fig. 7) can rotate the femur around its longitudinal axes and also can flex and extend the legs. This model was able to reproduce many turn techniques performed in actual skiing. That is, turn techniques such as snow plow turns, stem turns and parallel turns (wedeln) - in every case by upward and downward motions.

Fig. 7 Stem turn: Combination of flexion/extension
of the legs with femur rotation around its axis

3. A carving turn evokes when the shaped skis, which produces an effective side curve, was used and when it edged on a ski. Also reproduced by the robots were: the carving turn models also able to do adduction and abduction in the hip joints (Fig. 8), also able to do flexion and extension of the legs model (Fig. 9) and an inward-lean model (Fig. 10).


Fig. 8 A model of adduction and abduction in the hip joints	Fig. 9 A model of flexion and extension of the legs	Fig. 10 An inward-lean model

4. The top of the inside ski in a snow plow (skidding turn) is lifted as in fig. 11 (toplift model): performing a stem turn (skidding turn) the top of the inside ski is lifted, too (Fig. 12).


Fig. 11 A snow plow toplift model (Zehetmayer model)	Fig. 12 A stem toplift model

5. Inner rotation of the outside femur in a turn showed that it is the most important element for a turn in the skier's movement, thus having application to skiing instructions: from the femur rotation model, the combined model of the femur rotation with the flexion and extension of legs (Fig. 7), and the combined model of femur rotation with an adduction and abduction in the hip joints (Fig. 13). Moreover, as shown in Fig. 14, it was shown clearly that the system of the fundamental skiing postures and turn techniques could be summarized by aspect of femur rotation.


Fig. 13 A combined model of femur rotation with adduction and abduction in the hip joints


Fig.14 the system of the fundamental skiing postures and turn techniques

6. If the side-cut of the skis comes in contact with the snow by bending the snowboard, an 'effective side-curve' can occur. The snowboard then runs along this effective side-curve (carving turn). This model makes a downhill turn and a sequential uphill turn along the effective side-curve (Fig. 15). When a snowboarder is weighting intensively on the front part of a snowboard, the snowboarder/snowboard system (SS) is able to do a skidding turn (Fig. 16).


Fig. 15 A snowboard model with outriggers for repeated and automatic carving turns	Fig. 16 A snowboard model with outriggers for repeated and automatic skidding turns

7. The proto-type model of a snowboarding system leans forward (to the front-side) or backward (to the back-side). The proto-type model performs a front-side turn, when the model leans to the front-side, and the model performs a back-side turn, when the model leans to the back-side (Fig. 17): To perform a front-side turn, the model (Fig. 18) flexes the ankle (dorsi-flexion) and to perform a back-side turn, it extends the ankle (plantar-flexion). To perform a front-side turn, it extends the knee, and to perform a back-side turn, it flexes the knee (Fig. 19). To perform a front-side turn, it flexes the hip and to perform a back-side turn, it extends the hip (Fig. 20). By means of construction, use, observation and analysis of such models, we can conclude some important aspects to snowboard motion. For example, the edging and displacement of the snowboarder's center of gravity to the inside of a turn are the important motions for achieving turns at snowboarding. Especially through displacement of the snowboarder's center of gravity to the front side of a snowboard, a snowboarder's ability to make a skidding turn is facilitated.


Fig. 17 A proto-type model of a snowboarding system	Fig. 18 A model with dorsi-flexion (flexion) and planter-flexion (extension) of the ankles


Fig. 19 A model with flexion and extension of the ankles	Fig. 20 A model with flexion and extension of the hips