Boundary equation of the trajectory of a closed curve Are there analytical/closed form equations for the boundaries of the trajectory traced out by a closed curve (tool) in 2D plane? 
Refer to the attached image (The tool does not change orientation. It moves along a trajectory)



Perhaps one can find a point on g(x,y)=0 farthest along the normal of f(x,y) = 0 for every point on the trajectory of the tool.
 A: The key search term here is convolution, as essentially your tool $A$ is convolved
with the shape $B$ whose boundary is the curve.
The first paper below provides more than you need (in that your moving shape
is rigid):

In this paper we suggest an algebraic algorithm to compute the exact general sweep boundary
  of a  2D curved object which moves in its own $xy$ plane along a
  parametric curve trajectory while
  changing its shape parametrically. 
  In this case the general sweep boundary is composed of algebraic
  curve segments.
  
         
  


The second paper below is more specific to your question (despite its
non-descriptive title).


Kim, Myung-Soo, Jae-Woo Ahn, and Soon-Bum Lim. "An algebraic algorithm to compute the exact general sweep boundary of a 2D curved object." Information Processing Letters 47.5 (1993): 221-229.
Bajaj, Chanderjit, and M-S. Kim. "Generation of configuration space obstacles: The case of a moving sphere." IEEE Journal on Robotics and Automation 4.1 (1988): 94-99.

