Pink object has 3 degrees of freedom in its planar motion: two linear and one angular displacements.
This pantograph can deal with two linear ones.
Relations between coordinates of the object center A(X,Y) and coordinates of pistons ends B(t,0) and C(0,s):
x = (t+s.cosα)/2
y = (s+t.cosα)/2
α is angle between Ox and Oy
x and t are measured along Ox axis.
If α = 90 deg.
x = t/2
y = s/2
Angular position of the object is unstable and needs a control device (not shown).
Advantage of pantograph: no prismatic joints.