Universal Joint
Two shafts
AC
and
ED
, which lie in the vertical yz plane, are connected by a universal joint at
D
. The
bearings at
B
and
E
do not exert any axial force. A couple of magnitude 30 Nm (clockwise when viewed
from positive z axis) is applied to the shaft
AC
at
A
. At a time when the arm of the crosspiece attached
to the shaft AC is vertical determine (a) the magnitude of the couple
M
G
which must be applied to shaft
EG
to maintain equilibrium, (b) the reaction at
B
,
C
and
E
. (Hint: The sum of the couples exerted on the
crosspiece must be zero)
Solution
It helps to first decide how to categorize the structure. Because it has supports, it resembles the definition of
a frame. However, the structure also has moving parts (i.e., there is enough freedom of motion such that the
joint can swivel if you want it to) that transfer one load (the torque applied at
A
) into another (the torque at
G
). So it is really somewhere between a frame and a machine.
At any rate, since there are supports, we want to begin by drawing a FBD of the structure as a whole,
replacing the supports by equivalent reactions. The problem statement says that the bearings at
B
and
E
do
not support axial loads. So we let the components of reaction force along the axes of the shafts be zero at
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 Spring '08
 ORIENT
 Statics, Cartesian Coordinate System, Force, MD, shaft ABCD

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