(Dinosaur) Trains and Implicit Differentiation

This is just a demonstration of our implicit differentiation problem from class in order to get some insight on the problem.

Solve[(r *Cos[theta] - x)^2 + (r*Sin[theta])^2 == l^2,x] // InputForm

Linkage[l_,r_,theta_] := {ParametricPlot[{r*Cos[t],r*Sin[t]},{t,0,2*Pi}],Graphics[Disk[{r*Cos[theta],r*Sin[theta]},0.1]],
Graphics[Disk[{(2*r*Cos[theta]+Sqrt[2]*Sqrt[2*l^2-r^2+r^2*Cos[2*theta]])/2,0},0.1]],Graphics[{Thick,Line[{{0,0},{r*Cos[theta],r*Sin[theta]},{(2*r*Cos[theta]+Sqrt[2]*Sqrt[2*l^2-r^2+r^2*Cos[2*theta]])/2,0}}]}]};

Manipulate[Show[Linkage[2,1,theta],PlotRange->{{-1,4},{-1,1}}],{theta,0,2*Pi}]