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One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction.
The only line that fills the requirement is a line colinear with link P 1-A. Somewhere on this line there is a point P, the instant center of rotation for the body BAC. What applies to point A also applies to point B, therefore this instant center of rotation P is located on a line perpendicular to vector V B, a line colinear with link P 2-B.
Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. [1] [2] [3] Kinematics, as a field of study, is often referred to as the "geometry of motion" and is ...
A model of a robotic arm with joints. In robotics the common normal of two non-intersecting joint axes is a line perpendicular to both axes. [1]The common normal can be used to characterize robot arm links, by using the "common normal distance" and the angle between the link axes in a plane perpendicular to the common normal. [2]
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
A line (,) is completely defined by the ordered set of two vectors: a point vector p {\displaystyle p} , indicating the position of an arbitrary point on L {\displaystyle L} one free direction vector d {\displaystyle d} , giving the line a direction as well as a sense.
In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (radians), or one of the vectors is zero. [4] Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)