Animation of mechanisms with two or more degrees of freedom by A.B. Ivanov
Explanatory example.
The mechanism comprises a crank, of two connecting rods and slide,
is driven by a crank. Find all the provisions of the mechanism
for one complete revolution of the crank.
We will use the proposed AB Ivanov method which
is as follows.
We choose from six coordinates defining the position of the mechanism,
two, for example one of the coordinates of the end of the crank (x1) and the coordinate
slider (x6) .To transfer mechanism links from the position that
it takes at time t and which corresponds to the values
two coordinates x1, x6, infinitely close to the position he
holds at time t + dt, and which corresponds to the coordinates
x1 + dx1, x6 + dx6, you can proceed as follows.
At first we fix the coordinate x1, ie. to the four equations
geometrical constraints add the fifth equation x1 = 0, and move the
slider on the value dx6.
Then 6x increase, and x1 does not change.
Then move the end of the crank on the value of dx1, and fix the slide ,
fifth equation will now x6 = 0.
Repeat this procedure until, until we find all the provisions of the mechanism. .
Note that since the two coordinates of the six chosen arbitrarily
and optionally set the order of their alternation, there is
a plurality of solutions, of which two are presented in animations.



Planar three-link manipulator1

Planar three-link manipulator2

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2RC-2polsuna.smz (8,58 KiB) scaricato 1728 volta(e).

Robot Manipulator




TS serial chain.

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Puma Ploskaya.smz (63,22 KiB) scaricato 1795 volta(e).

Puma_Sphera 1.smz (70,3 KiB) scaricato 1674 volta(e).CS serial chain

Puma1

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Puma_Sphera 1.smz (64,66 KiB) scaricato 1630 volta(e).

Puma

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Puma.smz (64,2 KiB) scaricato 1711 volta(e).

Center triangular platform planar manipulator (shows two designs)
moves along a predetermined path rectangular.
For animation   was used the procedure A. B. Ivanov,
animations mechanisms with several degrees of freedom.

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RPRrestangle.smz (9,74 KiB) scaricato 1705 volta(e).

And in Maple

https://vk.com/doc242471809_380217387
https://vk.com/doc242471809_378352452
https://vk.com/doc242471809_379935473