Torque in Machine Design - MAELabs UCSD

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16 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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Torque in Machine Design


Torque and Moment play an important role in machine design. If a moving part jams, or a structure bends
when it is not suppose to, then the culprit is most likely to be excessive moments rather than purely
excessive force. A good
designer has an intuitive understanding of torque.


Torque relates to rotation. Thus, a force that tends to rotate an object applies a torque onto an object.
Since rotation occurs about a point, a torque is always calculated about a specified point. The eq
uation
for torque is given by the cross product between a Force vector,
F
, and a position vector,
D
, between the
point about which the torque is being calculated and the point at which the force is being applied. Thus:



=
F

x
D


This equation can also be
written in terms of the angle,

, between the vectors as:



= F D sin


An easy way to visualize torque is to imagine that a pin has been placed through the point about which
the torque is being calculated. Evaluate each force in terms of how it tends to ro
tate the object about this
imaginary pin. Those forces that would rotate the object counterclockwise are considered as positive
torque, while clockwise rotations are considered negative (according to the Right
-
hand rule convention).


There are two equally

correct methods to calculate the torque,

, about a point.


Method 1:



= F x D


F => force applied on body

D


=> the distance component that is perpendicular to the force vector


Method 2:



= F


x⁄

F


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D

=> distance from pivot to point where force is applied


The Free Body diagram (FBD) below shows both methods. Note that in a FBD one always shows the
force and torques in the direction applied
onto

the body being analyzed.




Visual Representation of Moments


A visual understanding of moments is especially important for machine design.
One

should be
able to look at a machine, and be able to
eva
luation the factors that contribute to moments.


Equation Representation


Definitions:


p = point about which moment
is being calculated (in this case
a pivot)

= vector from p to base of
force vector

= force v
ector



= angle between

and

M
p

= moment about p due to


Moment Equation


M
p

=

x

(cross product)



M
p

= Frsin








Perpendicular Force

Representation


Definitions:


= component of vector

that is perpendicular to vector
. (
= Fsin

).

= component of vector

that is parallel to vector
, which does not contribute to the
moment.

Moment Equation


M
p

=
r

Interpretation
: Only the perpendicular component

of F contributes to moments.



Moment Arm

Representation


Definitions:


= component of vector

that is
perpendicular to vector
, which is also the mo
ment arm

(
=rsin

)
.

= component of vector

that is parallel to vector
, which does not contribute to the
moment.

Moment Equation


M
p

=
F

Int
erpretation
: Only the
perpendicular

component

of r contributes to moments, and the
vector F
can be moved along its

axis without changing the moment.



Cartesian (XY)

Representation


Definitions:

r
x
, r
y

= x and y componen
ts of
.

F
x
, F
y

= x and y components of
.


Moment Equation


M
p

=

F
y

r
x


-

F
x

r
y

(note counterclockwise is positive with right
-
hand rule)