Plane Kinematics of Rigid Bodies Relative Motion Translating
Plane Kinematics of Rigid Bodies Relative Motion - Translating Axes - I Lesson 15 Section 5/6 • We have used the Relative Motion and Instantaneous Center of Zero Velocity methods to describe the velocities of points on a rigid body. • Let’s briefly review these methods. © D. J. Morrison, 2013 1
Instantaneous Center of Zero Velocity 1. Identify directions of velocity vectors of two points. 2. At these two points draw lines perpendicular to the velocity vectors. Meriam and Kraige, 7 th, Wiley 3. These lines intersect at the IC, point C. 4. If we know the magnitude of v. A or v. B you can solve for . © D. J. Morrison, 2013 2
Relative Motion -Translating Axes (Velocity) (Translating Frame) Absolute velocity of A wrt fixed frame (X, Y) y Absolute velocity of origin of the translating frame at B wrt fixed frame (X, Y) A/B Y x (Fixed Frame) X Fig 5/6 Meriam and Kraige, 7 th, Wiley © D. J. Morrison, 2013 Relative velocity of A wrt a translating frame (x, y) attached to B. If A and B are on the same rigid body, v. A/B = r. A/B 3
– Fixed Axis Rotation Review For any point on the rigid body, In vector form, Fig 5 -3 Meriam and Kraige, 7 th, Wiley Velocity Simulation © D. J. Morrison, 2013 4
Relative Motion -Translating Axes (Acceleration) y (Translating Frame) A/B x Y (Fixed Frame) X Fig 5/9 Meriam and Kraige, 7 th, Wiley © D. J. Morrison, 2013 Absolute acceleration of A wrt fixed frame (X, Y) Absolute acceleration of origin of the translating frame at B wrt fixed frame (X, Y) Relative acceleration of A wrt a translating frame (x, y) attached to B. Due to rotation about B if A and B are on the same rigid body. 5
y A/B x Y X Magnitude = r r 2 Fig 5/9 Meriam and Kraige, 7 th, Wiley © D. J. Morrison, 2013 6
Example Problem: L 15 -1 Given: FAS, =0, a 0=3 m/s 2 = 5 rad/s 2 Find: a. A when = 0º, Meriam and Kraige, 6 th, Wiley © D. J. Morrison, 2013 7
Example Problem: L 15 -2 Meriam and Kraige, 6 th, Wiley © D. J. Morrison, 2013 8
Example Problem: L 15 -2 Given: FAS, AO = 4 rad/sec AO = 0, = 60 Find: AB Simulation Meriam and Kraige, 6 th, Wiley © D. J. Morrison, 2013 9
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