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# Kinematics synthesis to design a mechanism for a wanted

Kinematics

Kinematics is the branch of physics that studies motion of systems
of bodies without considering or analysing forces and the causes of motion. Kinematics
is often referred as the “geometry of motion” and is often seen as a
branch of mathematics and sometime as the branch of mechanics. Using
arguments from geometry, the velocity, acceleration and speed of any parts of
the system that are unknown for us can be firmly determined by not changing it.
Kinetics is the study of how bodies fall within it.

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Kinematics
is used in astrophysics which is the branch of astronomy that is
concerned with the celestial bodies. In biomechanics kinematics, mechanical
engineering, and robotics describes the motion of systems composed of linked
components (multi-link systems) such as a human skeleton , an engine or
the robotic arm.

Geometric
transformations, are also called rigid transformation (a transformation
that doesn’t change the shape or size), which are used for describing, in
a mechanical system, the movement of components, making it to obtain  something from a source of the equations of
motion making it simpler or easier to understand. Furthermore, they are central
to dynamic analysis too.

Kinematic
analysis process the measuring of the kinematic quantities that is
used to describe motion. In engineering, for example, kinematic analysis can be
used finding the range of movement for a specified mechanism, and working
in the opposite way, using kinematic synthesis to design a mechanism
for a wanted range of motion. Furthermore, kinematics applies algebraic
geometry to the study of the mechanical advantage of a mechanism
or mechanical system.

Kinematics of a particle trajectory in a non-rotating frame of
reference

Mass is also expressed m, position
is also expressed r, velocity is also expressed v,
acceleration is also expressed a are classical particles of kinematic quantities.

The
study of the trajectory of a piece of matter is called Particle kinematics .
The location of a piece is determined as the coordinate vector from the place
where the coordinate frame begins, to the particle. For instance, imagine a
building that is 60 m South from your own house, which at your house is found
the coordinate frame, in a such way East is the x-direction and North is the
y-direction, then the coordinate vector to the base of the building is r =
(0, ?50, 0). If the building is 60 m high, then the coordinate vector to
the top of the palace is r = (0, ?60, 60).

Often,
a three-dimensional coordinate system is used to determine the location of a molecule.
Anyways, if the molecule is compelled to move in a place, a two-dimensional
coordinate system is enough. All examinations in physics are not completed
without those examinations being reported with respect to a reference frame.

The
location of a vector of a molecule is a vector drawn from the place where it
begins of the reference frame to the molecule. It shows both, the distance of
the location from the origin and its way from the from the beginning place.

The direction cosines (any of the cosines of
the three corners between a controlled line in an area) of the location of
the vector make available for use a quantitative measure of way. It is
important to see that the location of the vector of a particle isn’t special.
The position vector of a given molecule is unlikely relative to unlikely frames
of reference.

Velocity and speed

The velocity of
a molecule is a vector quantity that reports the way of the motion and the
magnitude of the motion of molecule. More mathematically, the rate of transformation
of the position vector of a point, with respect to time is the velocity of the
point. Think the ratio of the contrast of two positions of a molecule splitted by
the time interval, which is the average velocity over that time interval.

Velocity
is the time rate of alteration of the location of a point, and the dot indicates
the derivative of those functions x, y, and z with respect to time. Also, the
velocity is tangent to the trajectory of the molecule at every position the
particle settles along its path. See that in a non-rotating frame of reference,
the derivatives of the coordinate ways aren’t examined as their locations and
magnitudes are constants.

The
speed of a thing is the magnitude |V| of its velocity.

Acceleration

The
velocity vector can alter in direction and in magnitude or both at the same
tome. Thus, the acceleration is the rate of alteration of the magnitude of the
velocity vector plus the rate of alteration of way of that vector. The same
reasoning used with respect to the location of a molecule to determine
velocity, can be applied to the velocity to determine acceleration. The acceleration of
a molecule is the vector determined by the rate of alteration of the velocity
vector. The average acceleration of a molecule over a time interval is determined
as the ratio.

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion and Non-Uniform Motion

Uniform Motion:

Definition: Uniform motion is determined as the movement of a thing in
which the object travels in a straight line and its velocity is left
constant along that line as it encloses equivalent distances same intervals of
time, regardless of the length of the time.

Example:

1.If
the speed of a bus is 20m/s so the bus will do 20 meters is one second. The
speed is uniform after every second.

2.The
motion of the blades in a fan.

Non-Uniform
Motion:

Definition: Non
Uniform motion is determined as the movement of a thing in which the object
travels with varied speed and it doesn’t enclose same distance in equal time
intervals, irrespective of the time interval length.

Example:

1.A bus moving 16 meters in first two second and 26
meters in the next two seconds.

2.The motion of an airplane.

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