How is pantograph calculated?

How is pantograph calculated?

4 The pantograph equation and its solution =1,=∫x0(ay0(t)+by0(pt)+cy0(qt))dt=(a+b+c)x1!,=∫x0(ay1(t)+by1(pt)+cy1(qt))dt=∫x0(a(a+b+c)t+b(a+b+c)tp+c(a+b+c=(a+b+c)(a+bp+cq)x22!,=∫x0(ay2(t)+by2(pt)+cy2(qt))dt=(a+b+c)(a+bq+cq)(a+bp2+cq2)x33⋮

What is a pantograph in math?

A linkage invented in 1630 by Christoph Scheiner for making a scaled copy of a given figure. The linkage is pivoted at ; hinges are denoted . By placing a pencil at (or ), a dilated image is obtained at (or ).

What is the principle of pantograph?

The working principle of pantograph engraving machine is based on four bar mechanism in which one link is fixed and other links are pivoted. These other links move according to the movement of the tracing link. This is a low cost and high valuable apparatus.

How the pantograph works and how it is able to produce an enlarged image?

It’s based on parallelograms so that when moving one specified point, called the tracing stylus, along the outline of an image, an enlarged or reduced version of the image is created by the movement of another point, called the drawing stylus, which has a lead affixed to it.

How many degrees of freedom does a pantograph have?

The mechanism thus defined presents four degrees of freedom of movement: raising of the pantograph mechanism and bouncing, rolling and pitching movements of the pantograph head (Fig.

Why pantographs are used in trains?

Pantographs and overhead contact line contact points are used to ensure the uninterrupted and faultless transmission of electric energy from contact lines to running electric trains through pantographs.

What is the meaning Pantagraph?

Definition of ‘pantagraph’ 1. an instrument consisting of pivoted levers for copying drawings, maps, etc, to any desired scale. 2. a sliding type of current collector, esp a diamond-shaped frame mounted on a train roof in contact with an overhead wire.

How many links are in pantograph?

It consists of four links joined in such a way to form a parallelogram ABCD in which AB = CD and AD = BC. In the figure, OAE always remains in a straight line. Pantograph consists of four turning pair.

What is the coordinate system of a pantograph?

2. In any one position of the pantograph, one can lay down a “grid” of lines all parallel to the two directions determined by the links. This grid determines a “coordinate system,” something like the streets in a planned city. See Figure 2.

What is the difference between a pantograph and an eidograph?

The eidograph relocates the fixed point to the center of the parallelogram and uses a narrow parallelogram to provide improved mechanical advantages. The original use of the pantograph was for copying and scaling line drawings.

Why did Feynman use the analogy of a pantograph?

Richard Feynman used the analogy of a pantograph as a way of scaling down tools to the nanometer scale in his talk There’s Plenty of Room at the Bottom.

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