Nowadays, in the robotic field, cycloid gear actuator is one of the most commonly used. According to Nabtesco company

“transmission via cycloidal drive ensures high efficiency, a long life, and an extremely low backlash in gear”. These conditions are the main key of gear options.”

So, in this article, I will show you a basic knowledge of cycloid with its equation and calculation using Excel. We will deal with the Epicycloid and Hypocycloid. We will focus more on the main parameters needed to design the cycloid gears.

While creating and designing a cycloid gear, we mainly need:

• Gear ratio
• Eccentricity distance

So let’s get started

### 1. Epicycloid

According to Wikipedia, “In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. It is a particular roulette.”

The main equation of Epicycloid is

$$x(θ)=(R+r)\cos(θ)−r\cos((R+r)θ/r)$$

$$y(θ)=(R+r)\sin(θ)−r\sin((R+r)θ/r)$$

Which are

R : the main rolling radius which is

$$R=kr$$

r : Eccentricity

angle θ: in t

### 2. Hypocycloid

According to Wikipedia, “In geometry, a hypocycloid is a specific plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle.”

The main equation of Epicycloid is

$$x(θ)=(R-r)\cos(θ)+r\cos((R-r)θ/r)$$

$$y(θ)=(R-r)\sin(θ)−r\sin((R-r)θ/r)$$

Which are

R : the main rolling radius which is

$$R=kr$$

r : Eccentricity

angle θ: in t

These are the basic equation to show the cycloid path. We will start these equations in the upcoming article to generate the epicycloid and hypocycloid path using Microsoft excel. It is very important to know about the 2 cycloids because, in case of creating a cycloid ball reducer, both epicycloid and hypocycloid should be used. However, in case of creating of standard cycloid reducer with fixed pin, you will use only one of this path to reduce speed.

@mikaiaval

Epicycloid and Hypocycloid #Geogebra #Maths #Geometry #designtheory

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