226-Lect 6 - Week 6 Acceleration analysis graphical...

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1 Week 6 Week 6 Acceleration analysis - graphical method Acceleration analysis using (ch7, Norton) Week 6 Recalling the equations Velocity (of some point “P”): V P = V o + V + ω × R … Equation 8.16 And acceleration: A P = A o + A + 2 ω × V + α × R + ω × ( ω × R) … Equation 8.23 (M&R)
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2 Week 6 Graphical Method Graphical kinematic (motion) analysis basically consists of setting up a vector equation relating key points on a mechanism, and then laying out these vectors graphically. Velocity . .. V P = V Q + V PQ Generally the direction of each of the terms in the velocity equation can be deduced relatively easily - only one magnitude is required to complete the solution. Acceleration is less accessible to simple logic and observation. Week 6 Acceleration - Graphical Method The basic equation: A P = A Q + A PQ always true - the question is whether it can be evaluated. The simple equation can be expanded to: A p n + A p t = A Q n + A Q t + A PQ n + A PQ t + 2 ω V PQ NB this equation includes a Coriolis Acceleration term (2 ω V PQ ). It is relevant when both ω and V PQ are non-zero (may occur when there is a sliding connection between links).
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Week 6 Acceleration - Graphical Method Equation 7.4 in Norton is developed considering pin jointed 4 bar mechanisms only, hence the basic equation: A P = A Q + A PQ is expanded to: A p n + A p t = A Q n + A Q t + A PQ n + A PQ t Eq. 7.4 (Norton) And does not include the Coriolis term. A consistent way of correctly deciding about this is to use the fixed and rotating axes approach discussed last week. Week 6 Acceleration - Graphical Method A p n + A p t = A Q n + A Q t + A PQ n + A PQ t + 2 ω V PQ To solve the vector equation 8.31, it is necessary to determine the magnitude and direction of each term (leaving no more than 2 unknowns) - still use . A vector polygon can then be assembled to
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226-Lect 6 - Week 6 Acceleration analysis graphical...

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