Any technical system consists of interacting objects. In what follows, the notation x y ----------> A --------> means that object A is undergoing action x and is excerting action y. Let us introduce the following definition: objects A and B are called dual if x y y x -------> A ------> and -------> B --------> or x y -x -y -------> A ------> and -------> B -------->, where -x and -y are actions opposite to actions x and y respectively.For example, interactions between objects involved in the process of bending a metal pipe without caving its walls in, can be depicted as follows: R ___________ | | | | V A | A B --------> P ---------> F ^ | | R | |____________| where B denotes a machine that bends pipe, P denotes a pipe to be bended, and F denotes a filling material that fills the interior of the pipe and prevents the walls of the pipe from caving in; A means action and R means reaction to it.

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)A clarification added in 2004 in response to Pentti Soderlin questions:the above diagram is not a diagram of forces. It is a diagram of who acts and who reacts. The tool (bending machine) acts upon the pipe and being acted upon by it in return. The filling is, conversely, being acted upon by the pipe and acts on it in return.Since, R A A R --------->B----------> and --------->F---------> B and F are dual objects.

()A clarification added in 2004 in response to Pentti Soderlin questions:Since reacts to acts upon acts upon reacts to P------------->B-------------->P and P----------->F------------>P the opposite roles of B and F with respect to P is obvious.The analysis of various technological systems reveals that: A) dual objects can be of the following types: 1. heterogeneous dual objects ( i.e. they do not have common parts and have heterogeneous physical/chemical characteristics); 2. homogeneous dual objects (i.e. they are homogeneous from physica/chemical point of view but still do not have common elements/parts); 3. overlapping dual objects (i.e. they have common elements/parts); 4. absorbing dual objects (i.e. one of them is an element of another one); 5. coinciding dual objects (i.e. they are completely amalgamated/merged or the functions of one of them are delegated to another one); B) bettering of technological systems goes in the direction of amalgamating of dual elements/parts and subsystems, i.e. dual elements of type M are substituted by dual elemets of type N, where N > M.

For example, in the case of the above methods for bending pipes, it has been proposed recently to make the filling material to be a portion of the bending machine (transition from type 1 dual objects to type 4). It has been achieved by making use of a ferromagnetic pouder as a filling material and by applying electromagnetic force to it.

Another widely used method of the bettering of technological systems is to substitute the heterogeneous dual parts by the homogeneous ones. For example, if the following relationships happen in a technological system does not allow B to interact with ------------------------------------->C / / A \ \ protects from contacts with C ------------------------------------->B and A and B or A and C are heterogeneous, then the system can be improved in one of the following ways: - A is created from a portion of B or C; - A is made of the same material as B or C. An algorithms for searching new engineering solutions that employes analysis of dualities in technical systems looks as follows: Step 1. Draw a diagram of interactions between various elements of a system to be improved. Step 2. Single out dual elements (parts, subsystems). Step 3. Determine the type of relation between them. Step 4. Try to amalgamate/merge the dual objects and delegate the functions of one of them to another. Or at least make one of them a portion of another. If it does not go through, try to make them overlapping or make them homogeneous.