kinemaatika

Kinemaatika is a branch of classical mechanics that describes the motion of objects and systems without considering the forces that cause the motion. It uses quantities such as position, displacement, velocity, speed, and acceleration, defined with respect to a chosen reference frame and time.

The subject distinguishes translational (linear) motion and rotational motion. In translational motion, an object moves along a path through space; in rotational motion, a rigid body rotates about an axis. For a particle, the key variables are position r(t), velocity v = dr/dt, and acceleration a = dv/dt. ForRotation, angular position theta(t), angular velocity omega = dtheta/dt, and angular acceleration alpha = domega/dt are used, with tangential and radial components a_t = r alpha and a_r = r omega^2, and the linear velocity given by v = r omega.

Fundamental equations for constant linear acceleration in one dimension are s = s0 + v0 t + 1/2 a t^2, v = v0 + a t, and v^2 = v0^2 + 2 a (s − s0). For rotation, theta = theta0 + omega0 t + 1/2 alpha t^2, omega = omega0 + alpha t. The relationships between linear and angular quantities include v = r omega, a_t = r alpha, and a_r = r omega^2.

Kinematics underpins a range of fields, including robotics, computer animation, biomechanics, and vehicle dynamics. In robotics, forward kinematics computes the end-effector position from joint parameters, while inverse kinematics seeks the joint settings required to reach a desired position. Kinematic analysis also informs trajectory planning and motion sensing.