Mechanics of Machines MCB3043

Lecture 21: StaticForceAnalysisAP Dr Abdul Rahim Othman

Outline

Static Force Analysis Force Transmission Static Equilibrium 2-Force Member Force Analysis

Forces

Forces are transmitted from a machine member to another through contact surfaces. The contact surfaces might be in the forms of: A round pin turning in circular slot A round pin sliding or rolling in a linear slot Mating gear teeth Cam in contact with the follower A piston sliding in a cylinder A screw turning in a threaded hole

Force Transmission in Gears

Force Transmission in Cams

Force Transmission at Linkage Joints

Equilibrium

A link might be in a state of: static equilibrium if it is stationary dynamic equilibrium if it is moving at constant

velocity A mechanism is in a state of static equilibrium

if all its links are stationary

Static Equilibrium

For an object to be in static equilibrium, the following conditions apply:

sum of all external forces acting on the object F = 0;

sum of all moments about an arbitrary point on the object MA = 0

All machine members must be designed to be able to withstand the static load. To analyse for the static load on each member, the concept of static equilibrium must be applied to the machine member.

Static Force Analysis

Applicable when the linkage is: at rest moving at low speeds such that the

accelerations are low and thus the inertial forces generated in its members can neglected

2-Force Member

If an object is: in static equilibrium has only two joints (or contact points) to other links not subjected to an external force or torque,then the object is a 2-force member.

Presence of 2-force members in a linkage simplify the process of determining force directions in the force analysis

Force Analysis of a 2-Force Member

For a 2-force member to be in static equilibrium, the two forces at the two joints must:

have the same magnitude

act in opposite direction

act along the same line (otherwise M 0)

F = 0

M = 0

Force Analysis of a Linkage

A

A motor turns Link 2 about Joint A. Link 4 is supported by a spring to the frame.

The acceleration is low so that the inertial forces can be neglected.

Link 3 is the only 2-force member of the linkage so we have the information on the directions of forces acting at its joints.

F = 0 M = 0

Force Analysis of a Linkage

A

F = 0

M = 0

Force Analysis of a Rock Crusher

The rock crusher is moving slowly and thus the inertial force can be neglected. In the position shown, determine the torque required to drive the 60-mm link and crush the rocks. To crush the rocks, a force of 9000 N is required at the position shown.

Force Analysis of a Rock Crusher

Sketch the free body diagram for each moving link.

Solve the equilibrium equations for each link.

Free Body Diagrams

The angular positions can be obtained by drawing a scaled kinematic diagram of the linkage.

Reaction Forces at a Joint

Link 2 and Link 3 are joined at Joint B The reaction force of one link to another must be

equal in magnitude but in opposite direction Note the nomenclature: F32 is the force exerted by

Link 2 to Link 3

B

B

Free Body Diagram: Link 4

Link 4 should be analysed first because it contains the applied force, which is known.

Fx = 003.17cos13cos9000 4143 XFF

03.17sin13sin9000 4143 YFF Fy = 0

MD = 0

D

01807.65sin1309000 43 F

F43 = +7132 N 17.3 F41X = +1960 N F41Y = +96.3 N

Free Body Diagram: Link 3

F34 = +7132 N 17.3

F32 = +7132 N 17.3

|F34| = |F43|

Free Body Diagram: Link 2

Fx = 0

03.17cos2321 FF X Fy = 0

03.17sin2321 FF Y MA = 0

A

060)3.17cos( 2321 FT|F23| = |F32| F23 = 7132 N 17.3

T21=408561 Nmm = 409 Nm cw

Problem 13-11

A mechanism shown raises packages in a transfer mechanism. If a 100-N package sit on the horizontal link while the mechanism is stationary, determine the torque required from the motor. The weights of the links are negligible.

Ans: 28.9 Nm

Sliding Friction Force

frictional force should also be included in static force analysis

The force magnitude is Ff = N where is the frictional coefficient and N is the reaction force acting normal to the contacting surface

The direction of the force is opposite to the direction of motion (for dynamic friction) or potential motion (for static friction)

motion

FfN

Tutorial Week 12

13-12 13-15