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# lec08 - Instant Centers or Instantaneous Centers 1...

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 Instant Centers or Instantaneous Centers 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Thomas Peacock 3/5/2007 Lecture 8 Kinematics of Rigid Bodies Instant Centers or Instantaneous Centers “Point on a rigid body whose velocity is zero at a given instant” Instantaneous : May only have zero velocity at the instant under consideration. Idea : If we know the location of an instant center in 2D motion and we know the angular velocity of the rigid body, the velocities of all other points are easy to determine. Figure 1: Rigid body where I is the instant center. Figure by MIT OCW. v A = v I + ω × r IA = 0 + ω × r IA (1) v A = ω × r IA So body is undergoing rigid body rotation about I. How to locate an instant center? 1. Draw lines in direction of motion of two points on a rigid body. 2. Draw perpendiculars to both these lines at points.

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Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT
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lec08 - Instant Centers or Instantaneous Centers 1...

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