2 Replies Latest reply on Jun 1, 2012 10:26 AM by Chris Michalski

hello, i couldn't find anywhere better to ask this question as i'm going to use it in solidworks.

everyone knows how cycloid curve is generated. That is similiar but I don't know and couldn't find the name of the curve; that is generated by tracing a point on a rotating circle, which is simultaneously has a linear translation move independent of the given RPM (unlike cycloid).

one example can be a milling tool, contouring on a straight line. think of a tool with Ø10mm diameter, rotating 3000 RPM, has a feedrate of 300 mm/min. tool center coordinates are (5,0) at the beginning and i want to trace the point that initially positioned @ (10,0) for 5 seconds of movement.

• Re: Asking for an equation

Hi Can

I think you need a prolate cycloid, which is defined by a point outside a circle rolling on a line.

The diameter of your circle -- which would be theoretical and NOT your tool diameter - would be a function of the RPM and the feedrate.  In your example, this theoretical circle "rolls" 300mm for 3000 revolutions, i.e. 0.1mm per revolution.  Thus, its circumference must be 0.1mm and its diameter 0.1/pi mm.

Regards

Warren

• Re: Asking for an equation

Can -

I believe this is what you are looking for.  The x,y position of that point on a stationary rotating tool is a simple sine/cosine function - then add in the relative x-motion of the axis as a function of time.  I used a slower RPM because otherwise the graph gets really dense.