In this paper the method of transmission matrix is applied for investigating planar mechanisms [5-7]. As is known, in many engineering problems, for example, in the problem of synthesis and analysis of motion, the following problem is more and more interested. There is an object (a particle or body) connected with a frame of reference, which moves with respect to another frame. It is necessary to define the configuration (the position, velocity, acceleration) of the object under consideration in the latter frame. There are two types of the frame of reference. A frame that is fixed in time named inertia frame or global frame of reference and the frame attached to each body of the system- the body frame of reference. The problem is stated now as follows: Determine the configuration in global frame of a particle fixed in any body of the system.In this paper a method is constructed for solving such a problem by means of transmission matrices.The obtained results are illustrated by examples.

. In the paper [2] the method of transmission matrix applying for the case of a loop with turning pairs investigated. In the present paper the kinematics of a loop connected by composite joints, i.e. the one of revolute-translational joints are discussed now . By means of proposed method the planar motion of rigid bodies is presented by a point of general view . Especially,the introduced method allows to apply effectively universal softwere, for example, MATCAD, MAPLE, ... for investigating complex mechanical systems.

In the paper a new method to consider a mechanical system with non-ideal constraints is presented. It is proved that a mechanical system subjected to physical non-ideal constraints cannot be determined purely by theoretical analysis because the reaction forces depend on the physical parameters of interactive environment, which are defined only by measurement. The Principle of Compatibility is shown to be an effective tool in combination with experience for investigating such a problem. For illustration the dynamics of a digging machine are investigated.

This paper employ Khang’s definition of the partial derivative of a matrix with respect to a vector and the Kronecker product to define translational and rotational Hessian matrices. With these definitions, the generalized velocities in the expression of a linear acceleration or an angular acceleration are collected into a quadratic term. The relations of Jacobian and Hessian matrices in relative motion are then established. A new matrix form of Lagrange’s equations showing clearly the quadratic term of generalized velocities is also introduced.

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