This is what I did:
Given a bellcrank pivot at (0, 0, 0), the bellcrank arm at (0, d, 0), and the flap horn pivot at (a0, d, 0), with d and r0 being the bellcrank arm and flap horn lengths, respectively. Let the control handle and bellcrank arm be displaced by an angle of δ and the flap horn by α. Let θ = α - α0 be measured relative to the vertical. Both the flap horn and the plane of the bellcrank are initially canted forward α0 and α1 from the vertical, respectively. In general the bellcrank pushrod hole is located at (dSinδCosα1, dCosδ, dSinδSinα1) and the flap pushrod hole at (a0 + r0Sinθ, d, r0Cosθ). There is no influence from the lateral offsets of bellcrank and horn, even if they differ. This is easily visualized by imagining the pushrod to parallel the model’s centerline with an L shaped extension at the aft end to the horn. Let the pushrod length be
L = {[a0 + r0Sin(- α0)]^2 + [r0Cosα0]^2}^1/2 = [a0^2 - 2a0r0Sinα0 + r0^2]^1/2, evaluated at
α = δ = 0 (when θ = - α0), then
L^2 = a0^2 - 2a0r0Sinα0 + r0^2
After displacement
L^2 = [(a0 + r0Sinθ) - (dSinδCosα1)]^2 + (d - dCosδ)^2 + (r0Cosθ - dSinδSinα1)^2 . Expand , set equal and solve for δ. You'll have to read between the lines on subscripts.