take a hard look at picture take some fixed point anywhere on the circle and when the circle is rolled around the curve drawn by the the fixed point is the TROCHOID in the diagram i have drawn i labelled it as point D some where on circle also i have taken the angle to be "a"

Feb 20, 2016 · Cartesian equation of a trochoid. Ask Question Asked 9 years, 1 month ago. Modified 9 years, 1 month ago.

The involute is drawn with the base curve-involute intersection on the x axis. The two curves aren't in the same rotation space. In order to mirror the curve (across the x axis) into a whole tooth, I'm rotating the trochoid by pi/N radians and the involute by half a tooth (pi/2N) + the angle to the involute curve at the pitch diameter.

Since I have already outlined the general derivation for the circle-roulette with respect to a fixed curve in this answer, I will not repeat the derivation for this case, and instead present the necessary formulae for the "elliptic trochoid" corresponding to …

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Jun 7, 2015 · $\begingroup$ Matrices provide a nice framework for describing manipulations of systems of linear equations. Other than the practical advantages in actually working with a system of equations in matrix form, personally I find that form …

I know a trochoid has equations $ (x)t = at - b \sin{t} $ ; $ y(t) = a- b \cos{t} $ for trochoid of radius a and b distance from center of circle (According to Wolfram) The only speed equation I'm familiar with thus far in my study of parametric equations is the arc-length equation.

Experimental evidence suggests that the curve is a sort of trochoid. Here is a reference.. Specifically, it looks like the trajectory of a point in the interior of a disk which is rolling along a line, hence a "curtate trochoid" (N.B. personally, I'd have just called it a trochoid, but I think the crowd has it right here).

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