Machine Kinematics
solved, then drawn
Concept

Acceleration pole — where it appears

The point of a moving plane whose acceleration momentarily vanishes, which is a different point from the one whose velocity does. It is the one quantity in the field that depends on how the input is being driven, and on an ordinary four-bar it is never closer than a coupler length to the velocity pole.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Two poles at 66°, and only one of them is still. The stubs here are accelerations, not velocities, and they vanish at a different point from the one where the velocities vanish. The cross is the velocity pole — the point the plane is turning about — and the square is the acceleration pole, the point that is momentarily not accelerating. Over a full turn of this crank the two are never nearer than 1.49 coupler lengths and get as far apart as 22.2. The instantaneous centre is about velocities and about nothing else: the point that is not moving is being accelerated, usually hard, and a body pivoting about it in the ordinary sense would not be. positioned by solving, not by drawing.

The other pole

The instantaneous centre is the point of a moving plane that is not moving. There is a second point that is not accelerating, it is somewhere else entirely, and over a full turn of one four-bar the two are never closer than one and a half coupler lengths and get as far apart as twenty-two.

curvature · Curvature Two poles at 66°, and only one of them is still. The stubs here are accelerations, not velocities, and they vanish at a different point from the one where the velocities vanish. The cross is the velocity pole — the point the plane is turning about — and the square is the acceleration pole, the point that is momentarily not accelerating. Over a full turn of this crank the two are never nearer than 1.49 coupler lengths and get as far apart as 22.2. The instantaneous centre is about velocities and about nothing else: the point that is not moving is being accelerated, usually hard, and a body pivoting about it in the ordinary sense would not be. positioned by solving, not by drawing.

Six things a centre is not

The instantaneous centre is the most over-read object in this subject. Six claims about it are in circulation, three are false, two are true of something else, and one is nearly right — and each of them comes with a measurement of how badly it goes wrong.

wrong · Misconception

Named alongside it

The objects these essays reach for when they reach for this one.

CentrodeInstantaneous centreMoving planePath curvatureVelocity ratioContact orderPole tangentSecond-orderVirtual-work

All concepts