Epitrochoid

Epitrochoid

Geometry

Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

A circle rolling on another circle and exterior to it gives an epitrochoid. If a is the radius of the fixed circle, b that of the rolling circle, and k is the distance from P to the center of the rolling circle, the parametric equation of the epitrochoid is x=(a+b)cosθ-kcos((1+a/b)θ),y=(a+b)sinθ-ksin((1+a/b)θ). $$ x = (a + b){\text{~cos~}}\theta - k{\text{~cos~}}((1 + a/b)\theta ),\,\,\,y = (a + b){\text{~sin~}}\theta - k{\text{~sin~}}((1 + a/b)\theta ). $$

Fixed displacement gerotor oil pump (FDOP): a survey

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Journal Information

Published in International Journal of Ambient Energy, 2022

V.T. Gannesh, R. Sivakumar, G. Sakthivel

Generally gerotor profiles are developed based on the development method called ‘Trochoid’. Trochoid is defined as the locus of a point on the interior of a circular disc which rolls without slipping on a fixed circle. If the disc rolls on the outside of a circle, the locus of point B is an epitrochoid (Figure 2) and if the disc rolls on the inside of the circle, the locus is a hypotrochoid. Colbourne (1974) defined a parametric equation for epitrochoid and hypotrochoid with its envelope and illustrated the limitation of trochoid profile such as crossover formation when the locus point is outside the rolling circle and cup formation when the locus point is in the circumference of the circle.

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Fixed displacement gerotor oil pump (FDOP): a survey