BNG 202 – Biomechanics II

Lecture 15 – Relative Motion Analysis: Velocity

Instructor: Sudhir Khetan, Ph.D.

May 3, 2013

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

Afocus of today!

Kinematics of translation

• Kinematics– Position

– Velocity

– Acceleration

• True for all points in R.B. (follows particle kinematics)

B

AABAB rrr /

AB vv

AB aa

x

y

rB

rA

fixed in the bodySimplified case of our relative motion of particles discussion – this situation same as cars driving side-by-side at same speed example

Relative motion analysis: velocity

• Transl. & Rotation(General Plane Motion)

– Position

– Velocity (time deriv)• Let’s say motion of A is known• We would like to find motion of

B

and (ω is rotation of member about A)

A

B

ABAB rrr /

ABAB vvv /

x

y

rA

rB

dθdrA

drB

drA

rB/A rB/A (new)drB/A

ABAB rv //

why is this?translation rotation

where

Review of cross products

zyx

zyx

BBB

AAA

kji

BA

ˆˆˆ

or

• See Chapter 4 of your statics text for full details

Example Problem

If the block at C is moving downward at 4 ft/s, determine the angular velocity of bar AB at the instant shown.(F16-58, 2 rad/s)

Strategy: In beginning of the solution (“data” section should just be the sketch of the setup), what other information do we know about the components?

Example Problem

If rod AB slides along the horizontal slot with a velocity of 60 ft/s, determine the angular velocity of link BC at the instant shown. (F16-11, 48 rad/s)