This is an [b]Exact straight line drawing apparatus[/b] by "Hart's A-frame" principle※.[br](※ My principle: If bent angles relation [b]α=β[/b] were kept, then, the head draws a vertical line.)[br][br]Please drag the red bullet point ● C.[br] [ subject to ab=a'b', a[sup]2[/sup]+b[sup]2[/sup]-2ab cos(T0)-d[sup]2[/sup]= a'[sup]2[/sup]+b'[sup]2[/sup]-2a'b' cos(T0)-d'[sup]2[/sup]=0,[br] ----- below case is : ab=12, T0=90°, a=3, b=4, d=5, a'=6, b'=2, d'=√40 (=6.3245..)[br]--- [u]same[/u] product [b]ab=a'b'[/b], [u]same[/u] angle T, so [u]same[/u] area △ (∵ (1/2)ab sinT = (1/2)a'b' sinT). ]

[b]■ Bold Pink comment is very important:[br][/b]Pink --- image is a kind of shadow of its origin image.[br]Always exists.[br]It's complementary property (or duality). [br]Please feel next. (here, Point F is pale-green color top point.)[br]△EHF ∽ △BDF , & ratio HF : DF = CE : DF[br]△AIF ∽ △GCF , & ratio IF : CF = DA : CF[br]・・・ same ratio ( ∵ CE×CF = DA×DF --- so, CE/DF = DA/CF ⇒ q)[br]we define GB = q × AE , on purpose　( then, △AFE ∽ △GFB is true. [△GFB is rabatment type.])[br](Now "α = β" is not proved yet. but , "△CFE ∽ △DFB [by 3 edges same ratio]" and "△DFA ∽ △CGF [by 3 edges same ratio]" are proved. --- what will happen?[br]∠FDA = α ∈ △DFA, ∠FDB = β ∈ △DFB, ⇒ double character　∠DFA = ∠FDB = α = β. [br][b]conclusion "「α = β」 is always true." [/b] )[br] ( γ = ∠EFG,　δ = ∠AFB --　always, γ = δ )[br][ AE in pink figure will be rotated by rabatment. i.e. [b]orange color[/b], AE → AE', E' is on same circle. FE=FE', AE=AE' [br], So figure FGBDC is miniature of rotated FAE'H'I. ][br][br]IF you have this knowledge, it's easy to answer to next question.[br]Q1: What is DB length?[br]Q2: What is GB length?[br][br][b]Tip:[/b] Hart's A-frame top point F ● traces the exact straight vertical line to (horizontal) base segment AE or GB. There exists 2 apparatus in it. ---- i.e. recursive structure.[br][br][b]■ Comparison number of bars:[/b][br]1. Peaucellier Linkage --- 7 bars (exact straight-line)  vertical[br]2. Hart's Inversor --- 5 bars (exact straight-line)  vertical[br]3. Hart's A-frame --- 5 bars (exact straight-line)  vertical[br]4. Chebyshev Linkage --- 3 bars (approximate straight-line)  horizontal