Kinematics is the study of motion, without considering the forces which produce that motion. Kinematics of machines deals with the study of the relative motion of machine parts. It involves the study of position, displacement, velocity and acceleration of machine parts.
Dynamics of machines involves the study of forces acting on the machine parts and the motions resulting from these forces.
Plane motion: A body has plane motion, if all its points move in planes which are parallel to some reference plane. A body with plane motion will have only three degreesof freedom. I.e., linear along two axes parallel to the reference plane androtational/angular about the axis perpendicular to the reference plane. (e.g. linear along X and Z and rotational about Y). The reference plane is called plane of motion.
Plane motion can be of three types.
1. Translation
2. Rotation
3. Combination of translation and rotation.
Translation: A body has translation if it moves so that all straight lines in the body move to parallel positions. Rectilinear translation is a motion wherein all points of the body move in straight lie paths. E.g. the slider in slider crank mechanism has rectilinear translation. (Link 4 in fig.)
Translation, in which points in a body move along curved paths, is called curvilinear translation. The tie rod connecting the wheels of a steam locomotive has curvilinear translation. (link 3 in fig.)
Rotation: In rotation, all points in a body remain at fixed distances from a line which is perpendicular to the plane of rotation. This line is the axis of rotation and points in the body describe circular paths about it.
Translation and rotation:
It is the combination of both translation and rotation which is exhibited by many machine parts. (E.g. link 3 in Fig.)
Link or element: It is the name given to anybody which has motion relative to another. All materials have some elasticity. A rigid link is one, whose deformations are so small that they can be neglected in determining the motion parameters of the link. .
(a) Binary link: Link, which is connected to other links at two points. (Fig.a)
(b) Ternary link: Link which is connected to other links at three points. (Fig. b)
(c) Quaternary link: Link which is connected to other links at four points. (Fig.c)
Pairing elements: The geometrical forms by which two members of a mechanism are joined together, so that the relative motion between these two is consistent are known as pairing elements and the pair so formed is called kinematic pair. Each individual link of a mechanism forms a pairing element. Kinematic pair Fig.
Degrees of freedom (DOF)
It is the number of independent coordinates required to describe the position of a body in space. A free body in space (fig above) can have six degrees of freedom. I.e., linear positions along x, y and z axes and rotational/angular positions with respect to x, y and z axes. In a kinematic pair, depending on the constraints imposed on the motion, the links may lose some of the six degrees of freedom.
Types of kinematic pairs:
(i) Based on nature of contact between elements:
(a) Lower pair: If the joint by which two members are connected has surface contact, the pair is known as lower pair. E.g. pin joints, shaft rotating in bush, slider in slider crank mechanism.
(b) Higher pair: If the contact between the pairing elements takes place at a point or along a line, such as in a ball bearing or between two gear teeth in contact, it is known as a higher pair.
(ii) Based on relative motion between pairing elements:
1. Siding pair: Sliding pair is constituted by two elements so connected that one is constrained to have a sliding motion relative to the other. DOF = 13
2. Turning pair (revolute pair)
3. Cylindrical pair
4. Rolling pair.
5. Spherical pair.
6. Helical pair or screw pair.
Based on the nature of mechanical constraint
i. Closed pair
ii. Unclosed or force closed pair
Constrained motion: In a kinematic pair, if one element has got only one definite motion relative to the other, then the motion is called constrained motion.
(a) Completely constrained motion.
If the constrained motion is achieved by the pairing elements themselves, then it is called completely constrained motion
(b) Successfully constrained motion
If constrained motion is not achieved by the pairing elements themselves, but by some other means, then, it is called successfully constrained motion. E.g. Foot step bearing, where shaft is constrained from moving upwards, by its self weight.
(c) Incompletely constrained motion.
When relative motion between pairing elements takes place in more than one direction, it is called incompletely constrained motion. E.g. Shaft in a circular hole
Kinematic chain: A kinematic chain is a group of links either joined together or arranged in a manner that permits them to move relative to one another. If the links are connected in such a way that no motion is possible, it results in a locked chain or structure
Mechanism: A mechanism is a constrained kinematic chain. This means that the motion of any one link in the kinematic chain will give a definite and predictable motion relative to each of the others. Usually one of the links of the kinematic chain is fixed in a mechanism.
If, for a particular position of a link of the chain, the positions of each of the other links of the chain cannot be predicted, then it is called as unconstrained kinematic chain and it is not mechanism.
Machine: A machine is a mechanism or collection of mechanisms, which transmit force from the source of power to the resistance to be overcome. Though all machines are mechanisms, all mechanisms are not machines. Many instruments are mechanisms but are not machines, because they do no useful work nor do they transform energy. E.g. Mechanical clock, drafter.
Planar mechanisms: When all the links of a mechanism have plane motion, it is called as a planar mechanism. All the links in a planar mechanism move in planes parallel to the reference plane.
Degrees of freedom/mobility of a mechanism:
It is the number of inputs (number of independent coordinates) required describing the configuration or position of all the links of the mechanism, with respect to the fixed link at any given instant.
Grubler’s equation:
Number of degrees of freedom of a mechanism is given by F = 3(n-1)-2l-h.
where,
F = Degrees of freedom
n = Number of links = n2+ n3+……+n j, where, n2= number of binary links,
n3 = number of ternary links…etc.
l = Number of lower pairs, which is obtained by counting the number of joints. If more than two links are joined together at any point, then, one additional lower pair is to be considered for every additional link.
h = Number of higher pairs
Crank-rocker mechanism
Drag link mechanism
Double crank mechanism
Inversions of slider crank chain
Rotary engine – I-- inversion of slider cranks mechanism. (Crank fixed)
Whitworth quick return motion mechanism–I inversion of slider crank mechanism
Crank and slotted lever quick return motion mechanism – II inversion of slider crank mechanism (connecting rod fixed)
Oscillating cylinder engine–II inversion of slider cranks mechanism (connecting rod fixed).
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