Larger Radius of Hypocycloid given Chord Length Solution

STEP 0: Pre-Calculation Summary
Formula Used
Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
rLarge = lc/(2*sin(pi/NCusps))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
Variables Used
Larger Radius of Hypocycloid - (Measured in Meter) - Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.
Chord Length of Hypocycloid - (Measured in Meter) - Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
STEP 1: Convert Input(s) to Base Unit
Chord Length of Hypocycloid: 12 Meter --> 12 Meter No Conversion Required
Number of Cusps of Hypocycloid: 5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rLarge = lc/(2*sin(pi/NCusps)) --> 12/(2*sin(pi/5))
Evaluating ... ...
rLarge = 10.2078097002245
STEP 3: Convert Result to Output's Unit
10.2078097002245 Meter --> No Conversion Required
FINAL ANSWER
10.2078097002245 10.20781 Meter <-- Larger Radius of Hypocycloid
(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru
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4 Radius of Large Circle of Hypocycloid Calculators

Larger Radius of Hypocycloid given Area
Go Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))
Larger Radius of Hypocycloid given Chord Length
Go Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
Larger Radius of Hypocycloid given Perimeter
Go Larger Radius of Hypocycloid = (Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(8*(Number of Cusps of Hypocycloid-1))
Larger Radius of Hypocycloid given Smaller Radius
Go Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid

Larger Radius of Hypocycloid given Chord Length Formula

Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
rLarge = lc/(2*sin(pi/NCusps))

What is a Hypocycloid?

In geometry, a Hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the Hypocycloid becomes more like the cycloid created by rolling a circle on a line.
Any Hypocycloid with an integral value of k, and thus k cusps, can move snugly inside another Hypocycloid with k+1 cusps, such that the points of the smaller Hypocycloid will always be in contact with the larger. This motion looks like 'rolling', though it is not technically rolling in the sense of classical mechanics, since it involves slipping.

How to Calculate Larger Radius of Hypocycloid given Chord Length?

Larger Radius of Hypocycloid given Chord Length calculator uses Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)) to calculate the Larger Radius of Hypocycloid, Larger Radius of Hypocycloid given Chord Length is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the chord length of the Hypocycloid. Larger Radius of Hypocycloid is denoted by rLarge symbol.

How to calculate Larger Radius of Hypocycloid given Chord Length using this online calculator? To use this online calculator for Larger Radius of Hypocycloid given Chord Length, enter Chord Length of Hypocycloid (lc) & Number of Cusps of Hypocycloid (NCusps) and hit the calculate button. Here is how the Larger Radius of Hypocycloid given Chord Length calculation can be explained with given input values -> 10.20781 = 12/(2*sin(pi/5)).

FAQ

What is Larger Radius of Hypocycloid given Chord Length?
Larger Radius of Hypocycloid given Chord Length is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the chord length of the Hypocycloid and is represented as rLarge = lc/(2*sin(pi/NCusps)) or Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)). Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid & Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.
How to calculate Larger Radius of Hypocycloid given Chord Length?
Larger Radius of Hypocycloid given Chord Length is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the chord length of the Hypocycloid is calculated using Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)). To calculate Larger Radius of Hypocycloid given Chord Length, you need Chord Length of Hypocycloid (lc) & Number of Cusps of Hypocycloid (NCusps). With our tool, you need to enter the respective value for Chord Length of Hypocycloid & Number of Cusps of Hypocycloid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Larger Radius of Hypocycloid?
In this formula, Larger Radius of Hypocycloid uses Chord Length of Hypocycloid & Number of Cusps of Hypocycloid. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid
  • Larger Radius of Hypocycloid = (Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(8*(Number of Cusps of Hypocycloid-1))
  • Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))
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