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Unformatted text preview: ME 240
• Agenda:
– 17.3 – General Motions: Velocities – 17.5 – General Motions: Accelerations • For Friday
– HW (due 11/5): 17.31, 17.38 – Supplemental: 17.34, 17.48, 17.63 • Midterm Exam Credits – due Friday, 11/5 – 5 points possible (all or none) – Hand in brief (2‐3 sentences) explanations for the answer to each of the concept questions that you missed on the exam – Explanations must be typed – Concepts must be clearly explained with equations used, as needed, to support your argument • Midterm correction – question 1.7
– No units should have been given for masses or angles – If marked wrong on exam, please attach copy of first exam sheet to corrections handed in on Friday, or bring up after class or to my office hours Linkages ‐ Velocity
Velocity analysis of linkages:
4bar linkage: Slidercrank: We can use general approach to evaluate velocities using Velocity at joints is equal for the adjacent links Use mechanism constraints to help solve, examples: Velocity of fixed pivots is zero Velocity of sliding points is zero perpendicular to sliding motion 5‐20 Example: In the piston system shown, the crank AB has a constant clockwise angular velocity of 2000 RPM. AB = 2000 RPM
l1 l2 = 3 inch = 8 inch = 40 degrees Determine the velocity of point P on the piston for the configuration parameters given above 5‐21 Example: Given the angular velocity of link AB, AB= 3 r/s (CCW direction), at the instance shown determine the following: 1. Angular velocity of links BD (BD) and DE (DE) 2. Velocity of point G (on link BD) 5‐22 Planetary Gears
Gear Gear system that consists of one or more outer gears, or planet gears, revolving about a central, or sun, gear. • Sun – the central gear • Planet carrier • Annulus or ring Advantages over a traditional gearbox • Large reduction in a small volume • Load distribution (use multiple planets) • Multiple kinematic combinations • Pure torsional reactions • Coaxial shafting. Disadvantages • Inaccessibility • Design complexity
This example increases output speed. The planet gear carrier (green) is driven by an input torque. The sun gear (yellow) provides the output torque while the provides the output torque, while the ring gear (red) is fixed. Examples: Auto transmissions Non‐circular planetary gear system Given: sun gear radius rS=2 in., planet gear radius rP=0.67 in, the ring is fixed and the sun gear has angular velocity S=1500 rpm. Determine: the angular velocities of the planet and planet carrier: P and PC General Motion: Acceleration
Velocity of points on a rigid body: v A vB rA / B vA/B Acceleration of points on a rigid body: d a A aB rA / B dt drA / B dt v A / B rA / B (define angular acceleration) aA aB rA / B ( rA / B ) 2 Example: At the instance shown the angular velocity of the rigid body is 2 r/s CW and its angular acceleration is 3 r/s2 CCM. The rigid body rolls without slipping.
Determine: At the instance shown: a) The acceleration of point O. b) The acceleration of point G c) The location of the point whose acceleration is zero at the instance shown 5‐26 ...
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 Spring '08
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