226-Lect 9 - Week 9 MECH226 Phil Commins Week 9 Kinetic...

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1 week 9 1 Week 9 MECH226 Phil Commins Overview Week 9 – Kinetic analysis, analytical method Week 10 – Virtual work method Week 11 – Energy distribution method Week 12 – Balance of rotors and mechanisms week 9 2 Week 9 Kinetic Analysis Analytical Method Based on notes developed by Dr Oliver Kennedy – Presented by Phil Commins (Chapter 11, Norton) week 9 3 A O O B g g g 2 2 3 4 4 73.9 16.7 60 200 mm Superposition - Analytical Method Example Same example from Week 7 week 9 4 A O O B g g g 2 2 3 4 4 73.9 16.7 60 200 mm Superposition example Mechanism specs and problem outline. link length (mm) mass (kg) I (kg m ) 2 100 0.5 0.0005 3 200 1.0 0.004 4 150 0.75 0.002 Link 2 is driven at a constant speed of 100 rad/s in a cw direction. The centre of gravity of each link is at its geometric centre. Find the forces acting at the pin joints between each of the links, and the torque required to maintain the rotation of link 2 at this point in the mechanism's motion. The c.g. of each link is at its geometric centre. A = 1000 m/s A 2
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2 week 9 5 Steps in the analysis . .. 1. Carry out a motion analysis of the mechanism to determine the acceleration (linear and angular) of each link. 2. Determine the inertia forces and torques acting on each link. (NB these act to oppose the actual accelerations - the inertia force acts through the centre of gravity of the link, but may be offset to also provide the inertia torque. The offset approach is used when a graphical solution is being applied. If an analytical method is adopted, take moments about one of the joints { Σ M A = 0} .) week 9 6 Steps in the analysis . .. 3. Take one of the links - draw a free body diagram showing all the forces and torques acting on it (inertia and external, and forces acting from the other links at the joints). 4. Solve for any unknown forces (using 3 force and 2 force principles as appropriate). When complete this means that the forces acting on this link from the other links will be known . 5. Carry out a force balance at each of the remaining joints through the mechanism (NB during this stage of the solution, the remaining links are considered to be rigid massless connectors ) week 9 7 Steps in the analysis . .. 6. The forces and torques required throughout the mechanism to support the external and inertial loads on the link that is the subject of the analysis have now been determined. 7. Now put those results aside, and consider another link to be the subject of the analysis. Consider the external and inertial loads on this link, carry out force & torque balances as before. 8. Do this for each link - then collect all the results and superimpose the results to determine the combined loads (the force at each joint can be determined by a vector addition). week 9
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226-Lect 9 - Week 9 MECH226 Phil Commins Week 9 Kinetic...

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