Planimeter - Wikipedia
For the polar planimeter the "elbow" is connected to an arm with its other endpoint O at a fixed position. Connected to the arm ME is the measuring wheel with its axis of rotation parallel to ME. A movement of the arm ME can be decomposed into a movement perpendicular to ME, causing the wheel to rotate, and a movement parallel to ME, causing ...
Planimeters | National Museum of American History
This fixed-arm polar planimeter has a 4-1/2" tracer arm and 7" pole arm with cylindrical weight. It is made of German silver with a gold-colored coating. The tracer arm and pole arm are connected by a hinge and form a circle around the white plastic measuring wheel and vernier when the instrument is closed.
A polar planimeter can be used to measure a large region by placing its pole inside the region. (The pole is the fixed endpoint of the pole arm -- also the center of the circle followed by the left endpoint of the tracer arm.) When used in this way, the left endpoint goes all the way around the circle it follows, and so AL = r2,
Polar–Other - National Museum of American History
This German-made fixed-arm polar planimeter has a 4-1/2" metal and bronzed brass tracer arm and an 8" bronzed brass pole arm welded to a cylindrical weight. A carriage on the tracer arm has a white plastic measuring wheel, vernier, and registering dial.
The Planimeter and the Theorem of Green - Harvard University
2000年12月9日 · The polar planimeter is a mechanical device for measuring areas of regions in the plane which are bounded by smooth boundaries. The measurement is based directly on Green's theorem in multi-variable calculus: the planimeter integrates a line integral of a vector field which has constant curl.
The planimeter consists of 3 separate parts; the tracing arm to which is attached the roller housing the pole arm and the pole plate.The three parts are packed separately in the case. The pole arm is a simple beam. On each end is fixed a ball, one for …
Polar and Linear Planimeters - Wabash College
2004年1月2日 · This is done by making that point the hinge between the tracer arm and a secondary arm, one end of which (the pole) is fixed. The original polar planimeter was invented in 1854 by Jacob Amsler, a Swiss mathematician and inventor of many measuring instruments.
Keuffel & Esser 4236 Polar Compensating Planimeter
This German-made fixed-arm polar planimeter has a 4-1/2" metal and bronzed brass tracer arm and an 8" bronzed brass pole arm welded to a cylindrical weight. A carriage on the tracer arm has a white plastic measuring wheel, vernier, and registering dial.
Planimeters demystified - Mechanická matematika - MENDELU
For polar planimeter, one end of the moving line segment is fixed to a circle and the second one traces the boundary of the area. The fixation is managed by attaching the end to the end of another arm with fixed second end. This arm is able to …
Planimeter Applet Guide - hpmuseum.org
Point F is the pivot point, at the joint between the two arms. The arm joining points P and F is the pole arm. The arm joining points F and T is the tracer arm. The arms are of fixed length during a measurement. (Many models allow the tracer arm length to be adjusted between measurements; a few allow the pole arm to be adjusted.)
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