◀ Back to Note

Tony's Intertwingled Memex • Reference Manual

Mechanical Kinematics (Robotic Linkages)

Formulas & Definitions

A mechanical automation engineer is programming an industrial CNC plasma cutter on a manufacturing assembly line. The cutter head is constrained to move along an implicit elliptical track described by the equation:

4x2+9y2=364x^2 + 9y^2 = 36
where xx and yy represent coordinate positions in meters. During operation, optical telemetry confirms that the cutting head has reached the coordinate position:
(x,y)=(32,2)(x, y) = \left(\frac{3}{\sqrt{2}}, \sqrt{2}\right)

  1. Differentiate the implicit tracking equation with respect to xx using the Chain Rule to find an expression for the instantaneous tangent slope dydx\frac{dy}{dx}.
  2. Evaluate dydx\frac{dy}{dx} at the operational position (32,2)\left(\frac{3}{\sqrt{2}}, \sqrt{2}\right).
  3. Determine the required orientation angle and normal direction for the plasma cutting nozzle so that it cuts completely perpendicular to the elliptical track.