Instant Center of A Wheel Rolling Without Slipping
Consider the planar movement of a circular wheel rolling without slipping on a linear road; see sketch 3. The wheel rotates around its axis M, which translates in a direction parallel to the road. The point of contact P of the wheel with road does not slip, which means the point P has zero velocity with respect to point M. Thus, at the instant the point P on the wheel comes in contact with the road it becomes an instant center.
The set of points of the moving wheel that become instant centers is the circle itself, which defines the moving centrode. The points in the fixed plane that correspond to these instant centers is the line of the road, which defines the fixed centrode.
The velocity vector of a point A in the wheel is perpendicular to the segment AP and is proportional to the length of this segment. In particular, the velocities of points in the wheel are determined by the angular velocity of the wheel in rotation around P. The velocity vectors of a number of points are illustrated in sketch 3.
The further a point in the wheel is from the instant center P, the proportionally larger its speed. Therefore, the point at the top of the wheel moves in the same direction as the center M of the wheel, but twice as fast, since it is twice the distance away from P. All points that are a distance equal to the radius of the wheel 'r' from point P move at the same speed as the point M but in different directions. This is shown for a point on the wheel that has the same speed as M but moves in the direction tangent to the circle around P.
Read more about this topic: Instant Centre Of Rotation
Famous quotes containing the words instant, center, wheel, rolling and/or slipping:
“on the instant clamorous eaves,
A climbing moon upon an empty sky,
And all that lamentation of the leaves,
Could but compose man’s image and his cry.”
—William Butler Yeats (1865–1939)
“When the landscape buckles and jerks around, when a dust column of debris rises from the collapse of a block of buildings on bodies that could have been your own, when the staves of history fall awry and the barrel of time bursts apart, some turn to prayer, some to poetry: words in the memory, a stained book carried close to the body, the notebook scribbled by hand—a center of gravity.”
—Adrienne Rich (b. 1929)
“The wheel that squeaks the loudest
Is the one that gets the grease.”
—Josh Billings [Henry Wheeler Shaw] (1818–1885)
“On Linden, when the sun was low,
All bloodless lay the untrodden snow,
And dark as winter was the flow
Of Iser, rolling rapidly.”
—Thomas Campbell (1774–1844)
“There are those who would keep us slipping back into the darkness of division, into the snake pit of racial hatred, of racial antagonism and of support for symbols of the struggle to keep African-Americans in bondage.”
—Carol Moseley-Braun (b. 1947)