X = R cos 2v + (3/2)(e^2/R)(cos 8v - cos 4v)
+/- e(cos 5v + cos v)(1-(9e^2/R^2)sin^2 3v)^(1/2)
+/- (3/2)(ea’/R)(cos 5v - cos v)
+ a’ cos 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)
Y = R sin 2v + (3/2)(e^2/R)(sin 8v + sin 4v)
+/- e(sin 5v + sin v)(1-(9e^2/R^2)sin^2 3v)^(1/2)
+/- (3/2)(ea’/R)(sin 5v + sin v)
+ a’ sin 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)
These functions are cyclic functions with the period of 2π.
The inner envelope corresponds to:
v = (1/6)π ~ (1/2)π, (5/6)π ~ (7/6)π, (3/2)π ~ (11/6)π
Generally a’ can be determined as follows:
a’ = a - Sp
a: amount of parallel transfer of trochoid
Sp: minimum clearance between rotor and rotor housing
Here is the equation, plus background material
I attached the picture and also the link of the book
The book written by Kenichi Yamamoto the Chief engineer of Mazda, very well respected man who designed the rotary engine and he also later became the CEO of the Mazda company.
1981 by Kenichi Yamamoto, the father of the Mazda Rotary Engine
Equation 2.9 is the one i need to resolved for it builds the rotor. the Equation stars on page 12, with the actual equation on page 13.