Flat in Titwala : The planimeter, created in 1818 by surveyor-by-trade Johann Martin Hermann, follows the boundary curve with a pointed needle attached to a measuring wheel that adjusts the boundary length to the required length. The first practical, workable, and sophisticated planimeter was created in 1854 by Jacob Amsler-Laffon.

A basic tool for accurately determining the areas of any shape’s planar figures is a planimeter. To determine an area, trace the figure clockwise using the centre of the tracing lens (which is located inside the ring) and then read the result from the scales.

The tracing arm, the roller housing, the polearm, and the pole plate are the three components that make up the planimeter. The three components are packed separately in this instance. The polearm is an uncomplicated beam. One ball fits into the roller housing and the other onto the pole plate and is fastened to each end. Three components—a tracing lens, a measuring roller, and a supporting ball—support the roller housing.

 

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Different kinds of planimeter

The five main types are as follows:

Planimeter polar

A mechanical tool called a polar planimeter traces the perimeter of an area to determine its size. The measurement wheel, the tracer arm, and the polearm are the instrument’s three fundamental components. The measuring wheel is attach with its axis parallel to the tracer arm, the polearm revolves around the pole, and the tracer arm is connect to the free end of the polearm via a pivot joint.

A linear planimeter

A variation of the polar planimeter that measures the lengths of long, narrow zones is the linear planimeter.

Amsler polar planimeter

When measuring a region that is uneven or self-assertive in shape, the Amsler polar planimeter is useful. Keeping in mind the shape’s genesis, this device tracks the shape’s border. On the wheel at the hinge, the measurement is display.

digital planimeter

A sophisticated tool having a nickel-cadmium storage battery inside is a digital planimeter. An integrating wheel has been replace with a turning encoder in mechanical planimeters. The revolving encoder’s beats are calculate by an electrical circuit, and the area is shown on the display screen in digital form.

Prytz’s planimeter

This innovation was create in 1875. It is a relatively straightforward gadget made up of two rods having right angles on their ends. It was refer to by Prytz as a “stang planimeter,” which is Danish for “rod.”

Flat in Titwala : planimeter

How should I utilise a planimeter?

Place the record arm on the tracing arm precisely in the required scale using the clamp and movement screw.

Avoid utilising creased sheets for precision.

For little external upkeep, keep the anchor point on paper inside the border constant.

Place focus points and the tracing arm precisely along the external boundary line of the plan.

Get the Vernier, wheel, and dial’s initial readings. Once you reach the starting point, continue tracing the point along the plan’s perimeter.

As the tracing arm moves, observe zero rotations both clockwise and anticlockwise.

Before browsing, check the readings on the dial, wheel and Vernier again.

Flat in Titwala : planimeter

Planimeter: Factors influencing its accuracy

The accuracy of the device

Create a 100 square cm ellipse to check the precision of the instrument. To determine the ellipse’s area, follow the instructions. If the roller completely rotates from 0 (the initial point) to 0 (the terminus), the reading is accurate. To convert 1000 Vernier units to centimetres, multiply the result by 0.1. After running the test, we discovered that each reading would have a 0.1-percent error.

Environmental aspects

Accuracy is also affect by outside factors. Accurate results cannot be anticipate if the paper on which it is drawn is wrinkle or torn. The appropriate temperature is 20 °C (68 °F).

Human mistakes

Tracing requires focus and patience because trained people do better than untrained people. Results are also impact by daylight and a comfortable working position.

Area dimensions

While tracing a square with sides that are each 1 inches long and an error that is 0.01 inch results in a value of 1.04 square inches rather than 1 square inches, or a 4% error. Repeating the error with squares that have two sides yields a value of 4.08 square inches, or a 2% error. A 10-inch square has a result of 100.4 square inches, or a 0.4% inaccuracy. The rate of inaccuracy increases as the area increases.

 

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