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Unformatted text preview: ME 240: Dynamics Ch Chap. 17 Planar Kinematics of Rigid Bodies ME 240
– 17.1 Rigid bodies and types of motion – 17.2 Rotation about a fixed axis • Next week
– M, W: in‐class review for midterm exam – W 7:15pm, 1800 EH – Midterm Exam – Friday – ME Professional Development Day • Ch. 17 Problems
– HW (due 11/1): 17.4, 17.5 Why do we need to move to “rigid body” dynamics? r1 r
2 linkages R General mechanisms 5‐3 What are “rigid bodies”?
• A rigid body is a collection of particles that remain a fixed distance from each other (i.e., it does not deform – opposite of mechanics of materials!) How does rigid body analysis differ from particles?
• Rigid body analysis considers how the size and shape of the body affects both translational and rotational motion. Planar Rigid Body Motion
Planar motion – exists when all points in a body move within a plane Types of motion:
• General planar motion: degrees of freedom_____ • Pure Translation: each point in the body has the same velocity and acceleration • Rotation about a Fixed Axis: each point not on the axis of roation moves in a circular path. Motions The wheel: translation, rotation about fixed axis, or general plane motion? The piston: translation, rotation about fixed axis, or general plane motion? The connecting rod: translation, rotation about fixed axis, or general plane motion? wheel connecting rod piston Rotation About Fixed Axis
• Velocity of a point on a body rotating with angular velocity about a fixed axis v r • Acceleration of a point on a body rotating with angular velocity and angular acceleration about a fixed axis at r an r 2
• Gears: equating velocities at intersection point P r B A rB A B rA A rB Problem 17.3. Mass A starts from rest at t=0 and falls with a constant acceleration of 8 m/s2. When the mass has fallen one meter, determine: • Angular velocity of the pulley • Tangential and normal components of a point on outer edge of pulley 5‐8 A cyclist is contemplating switching from a traditional double crank (53/39 teeth on front gears) to a compact crank (50/36). Assuming the smallest gear on the back has 11 teeth and the largest has 25 teeth, determine the difference speed range between cranks when pedaling at 90 rpm. The wheel has a radius of 0.35m. 5‐9 ...
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- Spring '07