# 226-Lect 7 - Week 7 Outline Inertia force Foi = m ACGi...

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1 Week 7 Week 7 Kinetic (force) analysis (ch 11, Norton; ch 9 M & R) Week 7 Outline • Inertia force ( F oi = - m A CGi ) • Inertia torque (T oi = - I α i ) • Dynamic equilibrium • 2 force & 3 force members • Force & moment balances • Force couples • Principle of Superposition • Simultaneous Solution (matrix methods) Week 7 Inertia . .. Relates to the resistance a body exerts to a change of motion (acceleration) Linear motion: F = m A F o = - m A CG Note: the inertia force acts in the opposite direction to the acceleration (hence the negative sign) and it is based on the acceleration of the centre of gravity of the link Week 7 Inertia . .. Rotational motion: T = I α …T o = - I α Note: the inertia torque is in the opposite direction to the angular acceleration (hence the negative sign) and it is based on the angular acceleration of the link (which is not a specific property of a point on the link) Having completed the motion analysis theory, we are now in a position to determine relevant accelerations, and carry out force analyses including inertia effects.

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2 Week 7 Pure Rotation, constant ω ... Such as rotors, fans, propellers - represent a simple case. Centripetal acceleration only (A = ω 2 R) Inertia force = - m A t Ri Ro R dR b To determine the force required to hold a blade to the hub, need to add up (integrate) the inertia forces contributed by each bit of mass at each radius. Week 7 Force & Moment Balance For a body to be stationary (STATICS) the forces and moments acting on it must be in balance ( or EQUILIBRIUM) Forces = 0 (force polygon “closes”) Moments = 0 3 principles from statics: Week 7 Static Equilibrium 2 force body. .. If only 2 forces are acting on a body, the forces must exactly balance each other (same magnitude and line of action but opposite direction). Week 7 Static Equilibrium 3 force body. .. The 3 forces must intersect at a common point (otherwise taking moments about the point of intersection of 2 of the forces will result in the 3rd force having a net moment ). This principle often allows the direction of 3rd force to be found. NB the force polygon also must close.
3 Week 7 More than 3 forces acting . .. It is necessary to combine forces until only 3 are acting. For this to be possible the magnitude and direction of the forces to be combined MUST be known. The magnitude and direction of the resultant force can be found by constructing a force polygon . Week 7 More than 3 forces acting . .. The resultant of any set of forces acts through the point of intersection of the forces it is replacing. Resultant Week 7 Equilibrium - couples. .. A balanced pair of forces - offset from one another. Must be balanced by another couple providing an opposite torque. The location of the couple on the body does not matter. Week 7 Static Equilibrium These principles can be applied to determine the forces at joints and in links when mechanisms are held in static equilibrium while under external loads.

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4 Week 7 Dynamic Equilibrium We can make use of these static equilibrium principles in solving dynamic problems by . ..
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## This note was uploaded on 10/27/2009 for the course MECH 226 taught by Professor Weihuali during the Three '09 term at University of Wollongong, Australia.

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226-Lect 7 - Week 7 Outline Inertia force Foi = m ACGi...

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