Kinematics

The kinematics ( Greek: κίνημα kinematic movement ", of κινεῖν bringing cinema, move ') is the study of the motion of points and bodies in space, described by the variables position, velocity and acceleration, without looking at the causes of motion (forces ). The movement is generally due to constraints, such as the constant yarn length in a pendulum limited. Such kinematic bonds reduces the number of degrees of freedom of a body.

The motion of bodies under the action of forces is the subject of dynamics. Kinematics and dynamics are branches of mechanics. The kinematic analysis is the precursor for the preparation of the equations of motion, for example, according to the d' Alembert principle.

The sizes of the position, speed and acceleration at a rectilinear movement corresponding with rotational movement of the sizes angle, angular velocity and angular acceleration.

Motion of the mass point

The position of a point is defined by three coordinates in the three-dimensional space. Wherein a rigid body satisfy three further degrees of freedom for the rotation ( rotation in the three-dimensional space ) in order to describe the situation of the entire body.

The base of the kinematic equations of a point mass defining the speed and the acceleration as derivatives of the path curve, which passes through the position vector in the course of time:

If the motion is limited by kinematic bonds can be the position vector as a function of the generalized coordinates, which are summarized in the vector represent.

The rate is found to be by derivation of the position vector:

If you repeat this derivative the acceleration:

For the preparation of the equations of motion, for example, according to the d' Alembert principle, compatible with the kinematic bonds virtual displacement is required.

Absolute kinematics

The movement of rigid bodies, which are connected to one another by joints, is the basis for the analysis of multi-body systems. For this position, velocity and acceleration of the rigid body j are considered relative to body i. The relative movement ( generalized coordinates) and its derivatives are calculated by the joint co-ordinates. The movement variables of body i in the inertial frame are assumed to be known.

With:

Applications

For multi- body systems, the study of spatial mechanisms is the subject of kinematics. These mechanisms are often made of joints and connections. Examples are robots, kinematic chains and wheel suspension in the automobile industry. With kinematic methods ( in robotics, see Direct kinematics ) is determined the number of degrees of freedom and calculates position, velocity and acceleration of all bodies.