Using a Balancing Toy Pendulum for Teaching Rigid Body

Dynamics Tetsuya YAMADAShiga Prefectural Seta Technical High School

Fumiyasu KURATANIFaculty of Education, Wakayama University

Tadao YAMANOHyogo University of Teacher Education

From Shiga Prefecuture JAPAN

An inland industrial prefecture

There is big Lake Biwa

At Technical High Schools in Japan

Motion analysis as the

foundation of kinetic

design is not taken up.

A balancing toy pendulum is introduced as a practical example of a rigid body.

Simple Structure

The balancing toy is a traditional toy in Japan.It is simple structure.It isn't possible to move as the mind without the analysis.

A Balancing Toy Pendulum

Changing the angle between the arms modifies the position of the center of gravity and the moment of inertia of this pendulum.

Adjusting the machine screw in the center also modifies the distance between the position of the center of gravity and the supporting point.

Influence of the Center of Gravity and the Inertia Moment

a aGma

Φ

h

C

G

Oh

ab

Gb

ma

mb

222

2 )12

(222

1

hMbmlm

am

hMgf

bb

a

P

2222 2

1

22

2

2

1

ha

gh

hmam

ghmf

aa

aP

・・・ (1)

・・・ (2)

arm’s mass is neglected

arm’s mass is taken into consideration

Comparison between Theoretical and Measured Values

0 20 40 60 80 100 120

0.5

1.0

1.5

2.0

2.5

3.0

Na

tura

l Pe

rio

d T

(se

c)

(=1

/f)

Distance between the center of gravity of the whole model

a=125mmTheoretical Value

Measured Value

a=100mma=75mma=50mm

a=125mma=100mma=75mma=50mm

0

Range which can be made

h(mm)–

and the supporting point

It is clear that the theoretical and the measured natural periods show good agreement.

VIDEO 1

VIDEO 2

Lesson Practice

12 hours were spent on the lesson practice composed of subject explanation, theory explanation, motion analysis, design and making

We indicated the production of the balancing toy pendulum having the natural period of 1 second

Design and Production Goal

0 20 40 60 80 100 120

0.5

1.0

1.5

2.0

2.5

3.0

Na

tura

l Pe

rio

d T

(se

c)

(=1

/f)

Distance between the center of gravity of the whole model

a=125mmTheoretical Value

Measured Value

a=100mma=75mma=50mm

a=125mma=100mma=75mma=50mm

0

Range which can be made

h(mm)–

and the supporting point

A target is the natural period of 1 second.

In the Report

Almost all the students indicated the importance of analysis and design in manufacturing.

The Flowchart of Design and

Making

The distance between mass is determined

Start

AnalysisDesign

The distance between the center of gravityand the supporting point is determined

Assembly

Adjustment

Measurement

Evaluation

End

No

Ok

CONCLUSIONS This presentation has proposed the method of teaching rigid body dynamics. A balancing toy pendulum was introduced as a practical example of a rigid body.

The formula for calculating the natural frequency of a balancing toy pendulum was derived.

The theoretical and the measured natural periods of the balancing toy pendulum showed good agreement.

CONCLUSIONS 2

The natural period as a feasible objective in the design and making was illustrated.

The importance of analysis and design in manufacturing was highlighted by use this teaching material