226-Lect 4 - Week 4 Velocity polygon: eg 1 (1) Velocity...

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1 Week 4 Week 4 (1) Velocity analysis-graphical method (review) (2) Instantaneous Centres of Velocity (3) Velocity analysis - analytical method Week 4 Velocity polygon: eg 1 ω 2 =2 rad/s, O 2 A=3 cm, AB=8 cm, O 4 B=8cm Find V B , ω 3 and ω 4 Velocity polygon: eg 2 Week 4 Velocity polygon: eg 3
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2 Week 4 Instantaneous Centres of Velocity (sections 6.3-6.6 Norton, 8.12 – 17, M&R) • Concept • Kennedy’s Theorem • Velocity analysis using ICs Week 4 The concept… • An instantaneous centre of velocity always involves a pair of links • the 2 links are not necessarily in direct contact with each other • is a coincident point in space on the body of both links where the relative velocity between the 2 links is zero Week 4 The concept… • Is only valid for the instant that the links are in that position • These coincident points may not be on the physical body of the link - some imagination may be required. • For directly connected links, the location of these instantaneous centres can be determined by observation. Week 4 Directly connected links -3 ±cases±to±cons ider • Pin Connection – the pin joint itself is where both these links have the same velocity, and hence is the instantaneous centre for that pair • Rolling Connection – the point of contact between the wheel and the surface it is rolling on is the instantaneous centre for that pair
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3 Week 4 Directly connected links - 3 cases to consider •S l id ing Connect ion – The centre of curvature of the guide is the instantaneous centre between the link containing the guide and the slider – for “straight” slots this is at an infinite distance perpendicular to the slot. Week 4 Links NOT directly connected • One of the main advantages of this method is that it can be applied to links that are not directly connected - facilitating a fast solution • To find the location of these instantaneous centres Kennedy’s Theorem is applied. Week 4 A General Case Consider the ground as one link, and rigid body moving in plane curvilinear motion as the second.
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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 4 - Week 4 Velocity polygon: eg 1 (1) Velocity...

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