© t madas. what is an epicycloid? imagine a circle rolling on the outside of another circle. pick a...
DESCRIPTION
© T Madas cardioid cusp epicycloid with 1 cusp Heart-shaped Radius of rolling circle is equal to the radius of the fixed circleTRANSCRIPT
© T Madas
© T Madas
What is an epicycloid?Imagine a circle rolling on the outside of another circle.Pick a fixed point on the rolling circle and follow its path as the circle rolls all the way around.The curve it traces is called an epicycloid
This is not a unique curve.
We can get different epicycloids by:•changing the ratio of the radii of the two circles•changing the tracing point on the rolling circle
© T Madas
cardioid
cusp
epicycloid with 1 cuspHeart-shaped
Radius of rolling circle is equal to the radius of the fixed circle
© T Madas
nephroidepicycloid with 2 cuspskidney-shaped
cusp
cusp
The radius of rolling circle is half the radius of the fixed circle
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cardioid nephroid Cremona Curve
Epicycloids with 1 to 5 cusps
© T Madas
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© T Madas
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41 40 39 38 37 36 35 34 33 3231
3029
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2120
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98
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5431 74
144143142141140139
138137
136135
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© T Madas
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41 40 39 38 37 36 35 34 33 3231
3029
2827
2625
2423
22
2120
19
18
17
16
15
14
1312
1110
98
76
5431 74
144143142141140139
138137
136135
134
133
132
131
130
129
128
127
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122
121
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118117
116115
114113
112111 110 109 108 107 106 105 104
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8483
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146216215214213212
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CremonaCurve x
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© T Madas