Method of motion (1972)

The workshop of the plant.

Machines are working.

The mechanisms move relative to each other.

A mechanism is a connection of solid bodies, links in a certain way movably articulated with each other.

The movable connection of two links is called a kinematic pair.

The movable part of the lathe.

Various types of kinematic pairs in machine tools.

The relative movement of the links included in the kinematic pair depends on the design of the elements of the pair.

The nature of the relative motion of the links included in the kinematic pair is easy to find by applying the method of motion reversal.

A cartoon explaining the method of motion reversal.

Collage of various kinematic pairs.

Cartoon explaining the principle of movement of a free body in space.

A cartoon explaining the movement of a kinematic pair of a ball and a plane.

Such a pair is a Class 1 pair.

A cartoon explaining the movement of a kinematic pair of a ball and the surface of a half-cylinder.

Such a pair is a Class 2 pair.

A cartoon explaining the movement of a kinematic pair of a sphere and a hemisphere.

Such a pair is a Class 3 pair.

Those parts of the links that are in contact with each other are called elements of a kinematic pair.

A collage depicting kinematic pairs with various elements.

The elements of a kinematic pair can be a surface, a line, and a point.

An image of such elements.

Collage with frames dividing kinematic pairs into lower and higher ones.

A spherical pair with a finger of class 4 elements will have a surface and a line.

A single-movable rotary pair of class 5.

Collage of the display of kinematic pairs from grades 1 to 5.

Restrictions on rotational and translational movements can be imposed in various ways.

The screw pair also belongs to Class 5 pairs.

Samples of screw pairs.

The mechanisms are divided into flat and spatial.

In plane mechanisms, the trajectories of points lie in parallel planes.

Samples of such mechanisms.

In spatial mechanisms, these trajectories lie in non-parallel planes or are spatial curves.

Samples of such mechanisms.

Collage of images of kinematic pairs with their division into those belonging to spatial and planar mechanisms.

A cartoon explaining the method of analyzing a kinematic pair.

Screw pair in the machine.

An example of a kinematic pair of class 3.

It is not difficult to find the class of a kinematic pair if one of the links is a rack.

When both links are in motion, the class of the pair should be determined in the relative movement of the links included in the kinematic pair.

Samples of the movement of links.

A cartoon explaining the method of motion reversal.

A pair of connecting rod and piston is a kinematic pair of Class 5.

According to the method of reversing the movement of the pair, the end of the rocker arm and the cam profile is a kinematic pair of class 4.

Machines in the shop.

Gears are often used to transmit rotational motion.

The profiles of the teeth of two gears engaged in flat mechanisms form the highest kinematic pair of Class 4.

Usually the teeth on the wheels have an involute profile.

They can be performed by copying on a milling machine using a shaped milling cutter.

A feature of this method is the need to have a separate milling cutter for each wheel with its own number of teeth and module.

The method of cutting teeth without a shaped cutter is called the bending method.

A laboratory device that demonstrates the method of bending.

A cartoon explaining the envelope method.

The method of cutting gears using a gear rack is demonstrated.

The tool can also be a chisel - a gear wheel with cutting edges.

A cartoon explaining this method.

The movements of the chisel are controlled by a cam mechanism.

Cartoon explaining the law of motion of the driven link - dolbyak.

Cartoon explaining the law of motion of the driven link for the central cam mechanism.

As a result, we have obtained a cam profile that provides the required technological process.

The element of the kinematic pair on the pusher can be not only a roller, but also a plane.

Cartoon explaining the law of motion of the driven link - cam.

In a rotary automatic lathe, the feed of the caliper is regulated by a cam mechanism, but here the driven link is the rocker arm.

Cam mechanisms with a driven link - a rocker arm can have a very different design.

Oscillatory movements are performed around a fixed axis.

Cartoon explaining the law of motion of the driven link - rocker arm.

Motion reversal is effectively used not only in profiling gears and cams, but also in the study of the movement of complex mechanisms.

A helicopter lands.

Fixing the screw to the helicopter.

Mechanisms called gears are used to transfer rotational motion from one link to another.

It is possible to transfer movement from the leading link to the slave directly, or through a number of intermediate links.

There are multi-stage and single-stage transmissions.

A stage is a transmission that has only two links with fixed axes of rotation.

The gear ratio is the ratio of the angular velocity of one link to the angular velocity of another link, it is equal to the inverse ratio of the radii of the initial circles of the wheels.

The minus before the ratio of radii means that with such engagement of the wheels, the angular velocities have different directions.

Practically, the ratio of radii can be replaced by the ratio of the numbers of teeth.

The gear ratio of gears with internal gearing will be positive, because the angular velocities have the same sign.

A cartoon defining the formula of the gear ratio in a two-stage transmission.

There are mechanisms in which several transmission links rotate around movable axes.

Such mechanisms are called planetary.

A sample of a planetary mechanism.

Planetary mechanisms having a degree of mobility of more than one are called differentials.

A sample of the differential.

A cartoon explaining the simplest differential.

Cartoon explaining the five-link differential.

A cartoon explaining a five-link differential with internal gearing.

The property of differential mechanisms for two given differential speeds to find the third is used in calculating machines.

The differential mechanism is used in the drive of the driving wheels of the car.

This mechanism uses bevel gears.

When moving in a straight line, it can be assumed that the speeds of the wheels are equal, so the satellites do not rotate relative to their axes.

The box of the driver, together with the satellites, rotates as one.

When turning, the wheel rolling on the outside of the curve rotates faster than the wheel rotating on the inside curve.

The semi-axes will start rotating at different speeds.

The satellites begin to rotate around their axes and the whole mechanism turns into a differential.

By fixing one of the central wheels, we will get a single-stage planetary mechanism with one degree of freedom.

A cartoon explaining the operation of this mechanism.

Planetary mechanisms with one degree of freedom have found wide application in modern technology, due to the fact that, depending on their structure, it is possible to obtain small-sized systems with a large gear ratio or a higher efficiency compared to conventional gears.

The transmission mechanism of the helicopter propeller.