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Planar motion control 1b

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.

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