Download presentation

Presentation is loading. Please wait.

Published byMadeleine Wilkinson Modified over 2 years ago

1
BNG 202 – Biomechanics II Lecture 14 – Rigid Body Kinematics Instructor: Sudhir Khetan, Ph.D. Wednesday, May 1, 2013

2
Particle vs. rigid body mechanics What is the difference between particle and rigid body mechanics? – Rigid body – can be of any shape Block Disc/wheel Bar/member Etc. Still planar – All particles of the rigid body move along paths equidistant from a fixed plane Can determine motion of any single particle (pt) in the body particle Rigid-body (continuum of particles)

3
Types of rigid body motion Kinematically speaking… – Translation Orientation of AB constant – Rotation All particles rotate about fixed axis – General Plane Motion (both) Combination of both types of motion B A B A B A B A

4
Kinematics of translation Kinematics – Position – Velocity – Acceleration True for all points in R.B. (follows particle kinematics) B A x y rBrB rArA fixed in the body Simplified case of our relative motion of particles discussion – this situation same as cars driving side-by-side at same speed example

5
Rotation about a fixed axis – Angular Motion In this slide we discuss the motion of a line or body since these have dimension, only they and not points can undergo angular motion Angular motion – Angular position, θ – Angular displacement, dθ Angular velocity ω=dθ/dt Angular Acceleration – α=dω/dt Counterclockwise is positive! r

6
Angular velocity http://www.dummies.com/how-to/content/how-to-determine-the-direction-of-angular-velocity.html Magnitude of ω vector = angular speed Direction of ω vector 1) axis of rotation 2) clockwise or counterclockwise rotation How can we relate ω & α to motion of a point on the body? angular velocity vector always perpindicular to plane of rotation!

7
Relating angular and linear velocity http://lancet.mit.edu/motors/angvel.gif v = ω x r, which is the cross product – However, we don’t really need it because θ = 90° between our ω and r vectors we determine direction intuitively So, just use v = (ω)(r) multiply magnitudes http://www.thunderbolts.info

8
Rotation about a fixed axis – Angular Motion r Axis of rotation In solving problems, once know ω & α, we can get velocity and acceleration of any point on body!!! (Or can relate the two types of motion if ω & α unknown ) In this slide we discuss the motion of a line or body since these have dimension, only they and not points can undergo angular motion Angular motion – Angular position, θ – Angular displacement, dθ Angular velocity ω=dθ/dt Angular Acceleration – α=dω/dt Angular motion kinematics – Can handle the same way as rectilinear kinematics!

9
Example problem 1 When the gear rotates 20 revolutions, it achieves an angular velocity of ω = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required.

10
Example problem 2 The disk is originally rotating at ω 0 = 8 rad/s. If it is subjected to a constant angular acceleration of α = 6 rad/s 2, determine the magnitudes of the velocity and the n and t components of acceleration of point A at the instant t = 0.5 s.

Similar presentations

Presentation is loading. Please wait....

OK

PLANAR RIGID BODY MOTION: TRANSLATION & ROTATION

PLANAR RIGID BODY MOTION: TRANSLATION & ROTATION

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on division for class 3 Ppt on model view controller design Ppt on rainwater harvesting in india download Ppt on you can win michael Ppt on polynomials of 900 Ppt on first conditional and second Ppt on amway business plan Ppt on amplitude shift keying circuit Ppt on urinary tract infection in children Presentations ppt online viewer