ics and mechanical advantage (ma)engineering2.union.edu/~tchakoa/mer312/lectures/lecture... ·...

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

ICs and Mechanical Advantage (MA)

Lecture 8



Mechanical Advantage (MA)

The Mechanism is a conservative systemInertial and friction effects are ignored for the system



Examples



Mechanical Advantage

Definition: Ratio of force-out over force-inForce, Velocity, and Torque are typically constant for a linkage




Tin =Findin =Foutdout =Tout




M.A. is a product of two factorsRatio of distances that depend n the placement of the input and output forcesAn angular velocity ratio

Can be expressed entirely in terms of direct distancesBased on the instant center development




If we know the angular velocity ratio between the input and the output link, M.A. can be expressed entirely in terms of ratios of distances



M.A. and Instant Center

An angular velocity ratio can be expressed entirely in terms of direct distances

Based on the instant center development



M.A. and Instant Center

. .

in

out

in in

out out

Vrin

Vrout

in out

out in

dM Adddd rd r

ωω

= ⋅

= ⋅

= ⋅



Drive Mechanism Example

Handle is being pulled to left with force Fin

Pressure difference across the piston in the cylinder is resisting the movement by a force equal and opposite to Fout

dout

din



Solution

dout



Toggle Position



Example #2



MA for a Slider Crank

MA needs to be modifiedLink 4 Constrained to move in the horizontal directionFout is constrained to be in the horizontal direction

rin

din



MA Slider Crank

2 2 2

2 2

( ) ( )in out

out B B in

in in in out

out in

in in

Power Power

T F v where v rd F r F

F dMAF r

ω ωω ω

=

= = ⋅⋅ ⋅ = ⋅ ⋅

= =

rv r r ro o

rin

din



Six Bar Linkage

Determine the MA of this system



Instant Centers for 6 Bar Linkage



Can Crusher Example

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