MEE 519 Final Take-home Test Spring 2022 The two degree-of-freedom, planar, open-chain mechanism shown in the adjacent figure is to place point P at any desired planar location

MEE 519 Final Take-home Test

Spring 2022

The two degree-of-freedom, planar,

open-chain mechanism shown in

the adjacent figure is to place point

P at any desired planar location.

The mechanism is actuated by two

motors, providing torques T1 and

T2.

a. For a given ?1 and ?2 , find

the location of point P, i.e.

the coordinates X and Y of

point P.

The global

coordinate system

(frame x,y ) is

placed at point O.

b. Derive the equations of motion for the mechanism.

Use ?1 and ?2 as the generalized coordinates and T1 and T2 as the generalized forces

(torques).

Parameters:

? Mass of links 1 and 2 are m1, and m2, respectively. The mass of each link is uniformly

distributed along the length of the beam, i.e, the center of mass of each link is at its

center of geometry.

? Moments of inertia of links 1 and 2 around their centers of mass are J1 and J2 ,

respectively.

? Links 1 and 2 have the length l1 and l2 .