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Obtain the dynamic equations of the PR(Prismatic+rotarary) manipulator in the figure using the Lagrangian method.

1-derive the lagrangian equations of motion

2-calculate the kinetic and potential energy of the two point masses(mass1,mass2)

3-deritivates for one particular component of the lagrangian

4-write the vector equation of motion : Tau

I, w?
hi
RR Manipulator
V,
Mi
Wi
hz
dレ
M2 Vž t Ź-
V,(9)= Mi
,gh
h,
Vz Cq) =
Meghz
Trans fer
V, = Vat
W, = W, t
) =
Figure 10.8: The 2R robot arm.
u = M(q)q+ġ*r(q)ġ +g(q).
r,(4) =
ag

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