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Overrunning clutches are devices for transmitting rotary motion in one direction only. These mechanisms are widely used in automotive industry, for example, in torque converters, impulse stepless transmissions, inertial continuously variable transmissions, starter engine starting system, and in other similar devices, where torque transmission is performed only in one direction. There are many different designs of the overrunning clutches, for example, ball, roller, cam, ratchet, spring ones, etc. But despite such a variety of designs and great efforts to establish reliable overrunning clutches, these mechanisms are still the weakest parts of many drive systems. Therefore, creation of reliable overrunning clutches is an urgent problem of mechanical engineering. Unfortunately, existing designs of the overrunning clutches have insufficient reliability and durability, which in many cases limits reliability of drive as a whole.

The inertial continuously variable transmissions are mechanical transmissions that are based on the principle of inertia. These transmissions have a lot of advantages. Usually, the design of the inertial continuously variable transmissions consists of inertia pulsed mechanism with unbalanced inertial elements and two overrunning clutches. Dynamics of the transmissions is described by systems of substantial nonlinear differential equations. In general, precise methods of solution for such equations do not exist. Therefore, in practice, approximate analytical and numerical methods must be employed. The main analytical methods employ successive approximation, a small parameter, or power series expansion. Each approach has its advantages and disadvantages. Therefore, we need to compare them in order to select the best method for dynamic study of such kind of transmissions.

The inertial continuously variable transmission is a mechanical transmission which is based on the principle of inertia. This transmission has a lot of advantages, namely: compactness, minimum friction losses and high efficiency as a result of the relatively small number of rotating components, a wide range of transformation of the torque. It does not need any conventional friction clutches. This transmission protects the engine from overload when the output shaft is braked. This drive guarantees optimum conditions of work for the engine regardless of the changing of load, and smoothly changes output speed according to the load. Mostly, design of this transmission consists of a pulsed mechanism with unbalanced inertial units and two overrunning clutches. The objects of the investigation are structural dynamic analysis of the continuously variable transmission. The physical and mathematical models of this transmission are developed.

The inertial continuously variable transmissions are mechanical transmissions that are based on the principle of inertia. These transmissions have a lot of advantages. Usually, the design of the inertial continuously variable transmissions consists of inertia pulsed mechanism with unbalanced inertial elements and two overrunning clutches. Dynamics of the transmissions is described by systems of substantial nonlinear differential equations. In general, precise methods of solution for such equations do not exist. Therefore, in practice, approximate analytical and numerical methods must be employed. The main analytical methods employ successive approximation, a small parameter, or power series expansion. Each approach has its advantages and disadvantages. Therefore, we need to compare them in order to select the best method for dynamic study of such kind of transmissions.

The inertial continuously variable transmissions are transmissions of mechanical type. They have a number of advantages in comparison with other types of transmissions. For example, they have a big value of the coefficient of efficiency, since the principle of their action does not imply the need to convert energy from one type to another one. These transmissions have a compact design, a wide range of torque transformation. They can operate in direct mode, smoothing the torsional vibrations in the system. At the moment when the output shaft is stopped, the input transmission shaft continues to rotate, that prevents the engine from overloading. There are other advantages. But despite these advantages, the inertial transmissions are not widely used in the automotive industry. The main reason for this is the inadequate durability of the freewheel mechanisms involved in the designs of the inertial transmissions.

Overrunning clutches are devices for transmitting rotary motion in one direction only. These mechanisms are widely used in automotive industry, for example, in torque converters, impulse stepless transmissions, inertial continuously variable transmissions, starter engine starting system, and in other similar devices, where torque transmission is performed only in one direction. There are many different designs of the overrunning clutches, for example, ball, roller, cam, ratchet, spring ones, etc. But despite such a variety of designs and great efforts to establish reliable overrunning clutches, these mechanisms are still the weakest parts of many drive systems. Therefore, creation of reliable overrunning clutches is an urgent problem of mechanical engineering. Unfortunately, existing designs of the overrunning clutches have insufficient reliability and durability, which in many cases limits reliability of drive as a whole.

The inertial continuously variable transmission is a mechanical transmission which is based on the principle of inertia. This transmission has a lot of advantages, namely: compactness, minimum friction losses and high efficiency as a result of the relatively small number of rotating components, a wide range of transformation of the torque. It does not need any conventional friction clutches. This transmission protects the engine from overload when the output shaft is braked. This drive guarantees optimum conditions of work for the engine regardless of the changing of load, and smoothly changes output speed according to the load. Mostly, design of this transmission consists of a pulsed mechanism with unbalanced inertial units and two one-way clutches. The pulsed mechanism is well developed and possesses high reliability. However, the one-way clutches are the most unreliable parts of the transmission and restrain wide use of the transmission.