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## Abstract

The paper deals with the complete kinematical analysis of the mechanism that enters the machine tool structure designed to generate, in particular, plane surfaces. A machine tool of this kind is called shaping machine. For this purpose, Euler’s relations concerning the velocities distribution, written in projections on the fix reference system axes will be used. Starting from these relations we will get to a system of the first order linear differential equations whose unknowns are the kinematical parameters of the mechanism elements. The variation in time of these parameters will be obtained by solving the differential equations system the differential equations system using numerical integration methods.

## Abstract

The paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism. Starting from Euler’s relation concerning the distribution of speeds written in projections on the fixed reference system axes, a system of differential equations describing the movement of the mechanism was obtained. This system of differential equations was then solved using numerical integration methods and the variation with respect to time of the position kinematical parameters, of the velocities (the first order kinematical parameters), and of the accelerations (the second order kinematical parameters), was obtained. Matrix writing of the differential equations was used in order to make the differential equations set out in the paper easier to solve using the electronic computer.

## Abstract

The paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism, using the principle of virtual mechanical work for establishing the relations of connection between the kinematical parameters describing the movement of its elements.

## Abstract

The wheel is a very important machine part. It is very often found in the construction of the vehicles. Therefore its dynamics must be studied properly. In the paper is presented the dynamical survey of a wheel which climbs on an inclined plane under the action of an active moment produced by an engine. The case of rolling without sliding was taken under consideration in the paper. The approach of the problem is a numerical one. The differential equations describing the movement of the motor wheel were written in matrix form. The paper also presents a method of removing of the constraint forces from the differential equations of motion.

## Abstract

The kinematical study of mechanisms is a very important matter and therefore it must be done very properly. The slidercrank mechanism is very common in engineering applications. The present paper presents an incremental numerical method used for kinematical study of the aforementioned mechanism. The kinematics of the same mechanism is performed using an analytical method. In order to validate the incremental numerical method, the results obtained by using the two methods are then compared.

## Abstract

The present paper approaches in an original manner the dynamic analysis of a wheel which climbs on an inclined plane under the action of a horizontal force. The wheel rolls and slides in the same time. The two movements, rolling and sliding are considered to be independent of each other. Therefore we are dealing with a solid rigid body with two degrees of freedom. The difficulty of approaching the problem lies in the fact that in the differential equations describing the motion of the solid rigid body are also present the constraint forces and these are unknown. For this reason they must be eliminated from the differential equations of motion. The paper presents as well an original method of the constraint forces elimination.

## Abstract

The paper presents a numerical method of dynamic analysis of a wheel that moves along an inclined plane under the action of a motor torque. The wheel is regarded as a rigid solid body in plane motion that rolls and in the same time slides along a surface which is inclined relative to the horizontal with a certain angle of known value. Therefore, the wheel may be considered as a solid rigid body having two degrees of freedom. The movement of the wheel takes place under the action of a motor torque, active forces and link forces that are unknown. For this reason, link forces must be removed from the differential equations describing the movement of the wheel. The paper also presents a method of removing the link forces from the differential equations of motion.

## Abstract

When the dynamic study of a solid rigid body subjected to links is wanted to be performed, the main difficulty is that the differential equations of motion contain in their structure the constraint forces which are unknown. Therefore it is necessary to remove them from the differential equations that describe the motion of the rigid body. The case of a wheel climbing on an inclined plane has been presented in this paper. It is considered that the wheel is rolling without sliding on an inclined plane.