Basics of Robotics

3.1: What is kinematics?

3.2: Types of kinematic links
3.3: Kinematic pair/constrains.
Introduction to Kinematic
• Cambridge dictionary defines a machine as piece of equipment with
several moving parts that uses power to do a particular type of work.
• This definition gives us three ideas about a machine, which are:
• A machine is usually an assemblage of several parts.
• There exists relative motion between those parts.
• Machine as a whole does some work utilizing some form of energy.
• Now, let us look into each of those aspects of a machine, the first two
aspects together give an idea that a machine is made up of a number
of different parts or objects, and these parts moves relative to one
another. Any part of a machine that has a relative motion with
respect any other part is known as a kinematic link or link or element.
Introduction to Kinematic
• A kinematic link or simply a link need not be a single part or object; it
can be of several parts joined rigidly together with some kind of
fastening so that there is no relative motion. And also, the link need
not to be a rigid body; it should be a resistant body.
• Resistant bodies are bodies that can transmit forces without
significant deformation.
• For example, let us consider a ceiling fan; the down rod, that is the
vertical shaft of the fan that holds the portions below forms the first
link, whereas the blades, rotor, rotor housing, and the fasteners in it,
all of which together form the second link.
Types of kinematic links
• Any part of a machine that has a relative motion with respect other
parts can be termed as a link, but to fulfil the necessary conditions to
be termed as a link, that part should also be a resistant body.
• According to the nature of the link, it is mainly classified into 3 types,
which are rigid, flexible, and fluid links.
• Some literatures cite a fourth kind of link known as a floating link.
Rigid link
• Rigid links are those that can transmit the desired motion without
being deformed.
• They are an ideal kind of link concept mostly used in the design of
machines, and they do not exist in real world because friction and
dissipation effects are unavoidable during motion.
Flexible link
• Flexible links are those that can transmit the desired motion, but is
deformed without affecting its function.
• When the deformation of such links extends to an amount by which it
can affect the proper functioning, then it is repaired or replaced. For
example, belts, chains, springs, etc. belong to this category.
Fluid link
• Fluid links are those that use fluids to transmit motion.
• Fluids in properly designed passages and containers are pressurized
to transmit force in order to achieve the desired motion. Hydraulic
press, jacks, automobile brakes, etc. is a good example for this kind.
Floating link
• Floating links are those links that are not connected to a frame; in
other words, the links that are not connected to a fixed link.
• Links can also be classified into classified into binary, ternary, and
quaternary according to the number of links they are in contact with.
• A link that is connected to 2, 3, and 4 other links is called binary,
ternary, and quaternary link, respectively.
Kinematic pair
• Rigid body system is the term used to denote 2 or more rigid bodies
in space collectively.
• These rigid bodies can be coupled or paired together to restrict or
hinder some of degrees of freedom of the individual bodies so as to
obtain some desired movement.
• If 2 links of a machine are coupled together or in close contact and
produces a definite motion as a result of their mutual interaction,
then they are said to constitute a kinematic pair.
Kinematic pair
• The hindrance or restrictions placed on the maximum achievable
degrees of freedom of a link by means of pairing is known as
kinematic The term kinematic pair refers to kinematic constraints
between links.
Types of constrained motion
• According to the extent and limitations, there are 3 types of
constrained motions. They are:
• Incompletely constrained If the possible set of motion between a pair
can take place in more than 1 direction, then it is called incompletely
constrained motion.
• Completely constrained If the possible set of motion by a pair is
limited to a particular direction only, then it is called completely
constrained motion.
• Successfully constrained If the possible set of motion between a pair
is limited in direction and confined in it extend by some proper
means, then such motion is called successfully constrained motion.
Classification of kinematic pairs
• Kinematic pairs can be classified on the basis of the following:
• Nature of contact
• The relative motion
• The type of closure between the links.
Classification of kinematic pairs
Classification of kinematic pairs
• According to nature of contact between the links: Kinematic pairs can
be classified into lower pairs and higher pairs by the type of surface of
contact and its extent.
• Lower pair: If the 2 elements of a kinematic pair have a surface
contact, then such a pair is known as lower pair. Kinematic pairs
having sliding, turning, and screw pairs form lower pairs. Revolute
pairs and prismatic pairs are the 2 types of lower pairs common in
robots.
• Higher pair: If the 2 elements of a kinematic pair have a line or point
contact, then the pair is known as higher pair. Gears, belt drives, cam
and follower, etc. are good examples for higher pairs.
Classification of kinematic pairs
• According to the relative motion between the links: The freedoms of
motion enjoyed by the links in a pair can be considered as another criterion
for classification, by which they can be classified as follows:
• Sliding: If 1 element of a kinematic pair is completely constrained in such a
way that only sliding motion is permitted relative to other link of that pair,
then the pair is known as sliding pair. Piston cylinder arrangement is the
best example to understand sliding pair.
• Turning: When revolving or turning about an axis is the sole possible
movement between the 2 links of a kinematic pair, the pair is called turning
pair. The ceiling fan housing and blades revolving around the down rod, car
wheels revolving about its axle are some best examples for turning pair
Classification of kinematic pairs
• Rolling: In a pair, if 1 element rolls over the other, then is a rolling
pair. Ball and roller bearings are examples of rolling pair.
• Screw: The kinematic pair in which simultaneous revolution and
translation takes place as in a bolt turns in a nut is called screw pair
• Spherical: When 1 element of the pair is fixed and having a receptacle
shape, while the other one with spherical shape swivels in that, then
it is called a spherical pair. Example, ball and socket joint, pen stand,
etc.
Classification of kinematic pairs
• According to the type of closure: Kinematic pairs can also be classified
according to the type of closure between the elements as:
• Self-closed: If the required relative motion of a kinematic pair is solely
the outcome of the mechanical coupling or connection that exists
between them, then the pair is self-closed pair. All lower pairs are
self-closed pairs.
• Force-closed: When the 2 elements of a kinematic pair are held in
position while its functioning by the virtue of externally applied forces
and not by mechanical coupling, then the pair is force closed pair.