Machine Kinematics
solved, then drawn
Concept

Block and tackle — where it appears

A hoist made of one rope run back and forth between two blocks of sheaves, whose velocity ratio is the number of parts of line supporting the moving block. That integer is a limit rather than a value: the parts are not parallel, and each contributes only the cosine of its own lean.

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

A tackle's ratio, differentiated rather than counted. Four parts of line between two blocks 260 mm apart, drawn as one strand over real sheaves. The ratio a tackle is sold with is the number of parts supporting the moving block, and it is the limit of the true velocity ratio rather than its value: the parts are not parallel, so each of them shortens by less than the lift. Differentiating the run's own length gives 3.9471 here, 1.32% short of 4, and the gap closes as the blocks separate. positioned by solving, not by drawing.

A ratio that is a derivative of a length

A tackle is sold by counting the parts of line holding the moving block: four parts, four to one. Differentiate the strand's own length instead and a four-part tackle gives 3.927 with its blocks 220 mm apart and 3.617 at 90 mm — and the integer it is named for is a limit it reaches nowhere.

strands · Strand The number on the tackle is a limit. The velocity ratio of a 4-part tackle as its blocks separate, measured by differentiating the strand's own length. It is 3.6174 at 90 mm and 3.99992 at 6898 mm, and it reaches 4 nowhere. The shortfall is geometric and has nothing to do with friction: each part of line makes an angle with the lift, and a part at angle β shortens by cos β of the movement. A tackle used at close quarters — which is when a tackle is useful — is the case furthest from its own rating.

Six things a strand is not

A tackle that is not four to one, a wrap that is not a half turn, a tensioner whose travel takes up nothing, a winch speed that is not a property of the winch, a cable rig that holds nothing still, and a shaped pulley that cannot be asked for what it is usually asked for. Six claims, each with the number that kills it.

wrong · Misconception

Named alongside it

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

Design ruleReevingStrandVelocity ratioApproximationDerivativeIdlerInextensibleSlackSpoolSupport functionTendon

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