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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Radius of wheel, R		cm
Linear Speed of wheel, V		km/hr
Angle of select point on rim, θp		°

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Values	Units
♦  Velocity of center of wheel		m/s	Graphs:  Velocity magniture Vs Point location angle   Velocity direction Vs Point location angle   Acceleration Vs Point location
♦ Angular Velocity of wheel, ω		rpm
♦ Velocity of selected point, Vp		m/s
♦ Direction of velocity of the point, φp		°
♦ Magnitude of acceleration, Ap		m/s2
♦ Direction of acceleration, θp + 180		°

Kinematics of a Rolling Wheel

Consider a wheel rolling clockwise on a flat surface without skidding at a known linear velocity. The instantaneous velocity and acceleration vectors (magnitude and direction) are given by the following equations:

where
     x,y = coordinates of point P on the rim of the wheel
     θ = angular position of P, +ve clockwise with respect to the vertical
     R = radius of wheel
     V = constant linear velocity of wheel
     ω = constant angular velocity of wheel
     V_p = magnitude of resultant velocity vector at P
     φ_p = direction of resultant velocity at P
     A_p = magnitude of resultant acceleration vector at P
     t = time

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Mark's Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 10.
• Wolfe J; Rolling: the physics of wheels; 2004, www.phys.unsw.edu.au/~jw/rolling.html
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.