Kinematics of Machinery

Ramesh Kurbet, Asst. Prof. Department of ME, PESCE mandya
Kinematics of Machinery
Unit –I
Introduction to mechanisms and simple mechanisms
By: Ramesh Kurbet
Assistant professor
Department of Mechanical Engineering
PESCE, Mandya

Mechanism: Number of bodies/links are assembled in such a way that motion of one causes
constrained and predictable motion in the other link or body.
Machine: It is combination of mechanism, which apart from imparting definite motion to part,
also transmits and modifies the available mechanical energy into some kind of useful work.
Mechanism involves synthesis and analysis. Analysis is study of motions and forces concerned
with different parts of mechanism, where as synthesis involves design of different parts.
Kinematics: It deals with the relative motions of different parts of mechanism without considering
the forces producing the motions. So this study is only a geometric point of view study.
Dynamics: This involves calculation of forces impressed upon different parts of mechanism. The
forces may be either static or dynamic.
Dynamics can be further divided into two types,
Kinetics- It is the study of forces on body, when the body is in motion.
Statics- It is the study of forces on body, when body is at rest.

Rigid Body: A body is said to be rigid if under the action of forces, it does not suffer any distortion or
the distance between any two points in the body remains same.
Resistant Body: The bodies which are rigid for the purpose they have to serve( To do certain work).
Types of Constrained Motion
1.Completely constrained motion
• When the motion between a pair is limited
to a definite direction irrespective of the
direction of force applied, then the motion
is said to be a completely constrained
motion.
motion of a square bar in a square hole, as shown
in Fig a, and the motion of a shaft with collars at
each end in a circular hole, as shown in Fig.

2.Incompletely constrained motion
When the motion between a pair can take place in more than
one direction, then the motion is called an incompletely
constrained motion.
The change in the direction of impressed force may alter the
direction of relative motion between the pair.
3.Successfully constrained motion
When the motion between the elements, forming a pair, is such
that the constrained motion is not completed by itself, but by
some other means, then the motion is said to be successfully
constrained motion.
The motion of an I.C. engine the piston reciprocating inside an
engine cylinder are also the examples of successfully
constrained motion.

Link or Kinematic Link:
• Each part of a machine, which moves relative to some other part is known as a kinematic link (or
simply link) or element.
• Types: Rigid link, Flexible link, Fluid link
Characteristics of link: It must have relative motion and it must be a resistant body.
Types of link
Link with two Nodes : Binary Link (a)
Link with three Nodes : Ternary Link (b)
Link with four Nodes : Quaternary Link (c)

Kinematic Pairs / Joints
Kinematic pair is a joint of two links having relative motion between them. OR
Combination of two links such that their relative motion is completely
constrained.
Classification of Pairs:
 Based on nature of contact between links:
1. Lower Pairs -- Surface Contact
2. Higher Pairs – Point or Line Contact
Lower pair
When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element
slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning
pairs and screw pairs form lower pairs.
Ex: Nut turning on a screw, shaft rotating in a bearing, all
pairs of slider crank mechanism, universal joint, etc.

Higher pair
When the two elements of a pair have a line or point contact when relative motion takes
place and the motion between the two elements is partly turning and partly sliding, then the
pair is known as higher pair.
Ex: Toothed gearing, rope drives, ball bearing, roller bearing, cam and follower, etc.

 Based on nature of mechanical constraints:
1. Closed pair
2. Unclosed pair
1. Closed pair: When the elements of a pair are held together
mechanically, it is known as closed pair.
2. Unclosed pair: When the elements of a pair are in contact either
due to force of gravity or some spring action, they constitute an
unclosed pair.
Ex: Cam and follower pair (higher pair), screw pair, etc.
Ex: Cam and follower pair

 Based on nature of relative motion:
1. Sliding pair: sliding motion (Fig a) 2. Turning pair: turning or revolving motion (Fig b)
3. Rolling pair: rolling motion (Fig c) 4. Screw pair or helical pair: turning as well as sliding motion (Fig d)
5. Spherical or Globular pair : one link is in the form of sphere turns inside a fixed link (Fig e)

Types of Joints
• Binary Joint (B): If two links are joined at same connection, it
is called a binary joint. Joint ‘B’ indicates binary joint in the
diagram.
• Ternary Joint: If three links are joined at same connection, it is
called a ternary joint. It is considered equivalent to two binary
joints since fixing of any one link constitutes two binary joints
with each of the other two links. Joint ‘T’ indicates ternary joint
in the diagram.
• Quaternary Joint: If four links are joined at a connection, it is
called a quaternary joint. It is considered equivalent to three
binary joints since fixing of any one link constitutes three binary
joints with each of the other three links. Joint ‘Q’ indicates
quaternary joint in the diagram.
Note: In general, if n number of links are connected at a joint, it is equivalent to (n-1) binary joints

Degrees of Freedom
Consider a rigid body in space, how many motions the rigid body can have ??
1. Three translational motions along any three mutually perpendicular axes x, y and z
2. Three rotational motions about the axes x, y and z
‘Degrees of freedom of a pair’is defined as the number of independent
relative motions, both translational and rotational a pair can have’.
Degrees of freedom of a pair = 6 – number of restraints

Classification of Kinematic Pairs
Class Kinematic Pair No. of
Restraints
Restraints on Figure
Translatory motion Rotary motion
I Sphere - Plane 1 1 0 a
II Sphere - Cylinder 2 2 0 b
Cylinder - Plane 2 1 1 c
III Sphere 3 3 0 d
Sphere – slotted Cylinder 3 2 1 e
Prism - Plane 3 1 2 f
IV Slotted Sphere 4 3 1 g
Cylinder 4 2 2 h
V Cylinder (Collared) 5 3 2 i
Prismatic 5 2 3 j

Grubler’s criterion:
Mobility of Mechanism defines number of degrees of freedom.
DOF in space is given as
F=6(n-1)- 5j1-4j2-3j3-2j4-j5
Most of the mechanism are in two dimensional with two translational motion along two axes and one
rotational about one axis.
Therefore for a planar mechanism DOF is given by
F=3(n-1)-2j1-j2
If F<0, is a indeterminate or super structure
F=0, is a determinate structure
F>0, is a Mechanism

Find the DOF of following Mechanisms

Kinematic Chain
Kinematic Chain is an assembly of links in which the relative motions of the links are possible
and the motion of each relative to the other is definite.
Inversion of Mechanism
When one of link is fixed in a kinematic chain, it is called a mechanism. So we can obtain as many mechanisms as
the number of links in a kinematic chain by fixing, in turn, different links in a kinematic chain. This method of
obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the
mechanism.

(a) Four - bar Chain, (b) Six - bar chain and (c) Eight – bar Chain
In case of the motion of a link results in indefinite motions of other links, it is a non-kinematic chain
(d) Six - bar chain (non-kinematic chain)
A redundant chain does not allow any motion of a link relative to the other link
(e) Redundant chain

Linkage, Mechanism and Structure
Linkage is obtained if one of the links of a kinematic chain is fixed to the ground.
If motion of any of the movable links results in definite motions of the others, the linkage is known as a mechanism
If one of the links of a redundant chain is fixed, it is known as a structure or a locked system.

Types of Kinematic Chains
The most important kinematic chains are those which consist of four lower pairs, each pair being a sliding
pair or a turning pair. The following three types of kinematic chains with four lower pairs are important
from the subject point of view :
1. Four bar chain or quadric cyclic chain,
2. Single slider crank chain, and
3. Double slider crank chain.
1. Four bar chain or quadric cyclic chain,
Case-1: l>s+p+q Impossible to have a mechanism
Case-2: s+l<p+q Class-I Mechanism
1)Link adjacent to crank is fixed, will obtain crank- lever mechanism, called as rotary- oscillatory converter.
2)Crank is fixed, will obtain double crank or crank-crank mechanism, called as rotary-rotary converter.
3)Lever is fixed, will obtain double lever or lever-lever mechanism, called as oscillatory-oscillatory converter.
Case-3: s+l>p+q Class-II mechanism Produces Double lever mechanism.
Case- 4: Two bars are parallel and equal in length , Double crank mechanism

Inversions of Four Bar Chain
1. Beam engine (crank and lever mechanism).
A part of the mechanism of a beam engine (also known as crank and lever
mechanism) which consists of four links, is shown in Fig. In this mechanism,
when the crank rotates about the fixed centre A, the lever oscillates about a
fixed centre D. The end E of the lever CDE is connected to a piston rod which
reciprocates due to the rotation of the crank. In other words, the purpose of
this mechanism is to convert rotary motion into reciprocating motion. Fig.. Beam engine.
2. Coupling rod of a locomotive (Double crank mechanism).
The mechanism of a coupling rod of a locomotive (also known as double crank
mechanism) which consists of four links, is shown in Fig.
In this mechanism, the links AD and BC (having equal length) act as cranks and
are connected to the respective wheels. The link CD acts as a coupling rod and
the link AB is fixed in order to maintain a constant centre to centre distance
between them. This mechanism is meant for transmitting rotary motion from one
wheel to the other wheel.
Fig. Coupling rod of a locomotive

3. Watt’s indicator mechanism (Double lever mechanism).
A Watt’s indicator mechanism (also known as Watt's straight line mechanism or
double lever mechanism) which consists of four links, is shown in Fig.
The four links are : fixed link at A, link AC, link CE and link BFD. It may be noted
that FB and FD form one link because these two parts have no relative motion
between them. The links CE and BFD act as levers. The displacement of the link
BFD is directly proportional to the pressure of gas or steam which acts on the
indicator plunger. On any small displacement of the mechanism, the tracing point
E at the end of the link CE traces out approximately a straight line.
The initial position of the mechanism is shown in Fig. by full lines whereas the
dotted lines show the position of the mechanism when the gas or steam pressure
acts on the indicator plunger.
Fig. Watt’s indicator
mechanism

Single Slider Crank Chain
A single slider crank chain is a modification of the basic four bar chain. It consist of one
sliding pair and three turning pairs. It is usually, found in reciprocating steam engine mechanism.
This type of mechanism converts rotary motion into reciprocating motion and vice versa.
In a single slider crank chain, as shown in Fig., the links 1 and 2, links 2 and 3, and links
3 and 4 form three turning pairs while the links 4 and 1 form a sliding pair.
The link 1 corresponds to the frame of the engine, which is fixed. The link 2 corresponds to the crank ; link 3
corresponds to the connecting rod and link 4 corresponds to cross-head. As the crank rotates, the cross-
head reciprocates in the guides and thus the piston reciprocates in the cylinder.
Fig. Single slider crank chain.

Inversions of Single Slider Crank Chain
Single slider crank chain is a four-link mechanism. We know that by fixing, in turn, different links in a
kinematic chain, an inversion is obtained and we can obtain as many mechanisms as the links in a
kinematic chain. It is thus obvious, that four inversions of a single slider crank chain are possible. These
inversions are found in the following mechanisms.
1.Pendulum pump or Bull engine. In this mechanism, the inversion is obtained by fixing the cylinder
or link 4 (i.e. sliding pair), as shown in Fig. In this case, when the crank (link 2) rotates, the
connecting rod (link 3) oscillates about a pin pivoted to the fixed link 4 at A and the piston attached
to the piston rod (link 1) reciprocates. The duplex pump which is used to supply feed water to boilers
have two pistons attached to link 1, as shown in Fig.
Fig. Pendulum pump.

2. Oscillating cylinder engine.
The arrangement of oscillating cylinder engine mechanism, as shown in Fig., is used to convert
reciprocating motion into rotary motion. In this mechanism, the link 3 forming the turning pair is fixed.
The link 3 corresponds to the connecting rod of a reciprocating steam engine mechanism. When the crank
(link 2) rotates, the piston attached to piston rod (link 1) reciprocates and the cylinder (link 4) oscillates
about a pin pivoted to the fixed link at A.
Fig. Oscillating cylinder engine.

3. Rotary internal combustion engine or Gnome engine.
Sometimes back, rotary internal combustion engines were used
in aviation. But now-a-days gas turbines are used in its place.
It consists of seven cylinders in one plane and all revolves about
fixed centre, as shown in Fig., while the crank (link 2) is fixed.
In this mechanism, when the connecting rod (link 4) rotates, the
piston (link 3) reciprocates inside the cylinders forming link 1. Fig. Rotary internal combustion engine.
4. Crank and slotted lever quick return motion mechanism.
This mechanism is mostly used in shaping machines, slotting machines and in rotary internal combustion engines. In
this mechanism, the link AC (i.e. link 3) forming the turning pair is fixed, as shown in Fig. The link 3 corresponds to
the connecting rod of a reciprocating steam engine. The driving crank CB revolves with uniform angular speed about
the fixed centre C. A sliding block attached to the crank pin at B slides along the slotted bar AP and thus causes AP to
oscillate about the pivoted point A. A short link PR transmits the motion from AP to the ram which carries the tool
and reciprocates along the line of stroke R1R2. The line of stroke of the ram (i.e. R1R2) is perpendicular to AC
produced. In the extreme positions, AP1 and AP2 are tangential to the circle and the cutting tool is at the end of the
stroke . The forward or cutting stroke occurs when the crank rotates from the position CB1 to CB2 (or through an
angle β) in the clockwise direction. The return stroke occurs when the crank rotates from the position CB2 to CB1 (or
through angle α) in the clockwise direction. Since the crank has uniform angular speed, therefore,

Fig. Crank and slotted lever quick return motion mechanism.
Since the tool travels a distance of R1 R2 during cutting
and return stroke, therefore travel of the tool or length of
stroke .
Note: From Fig. we see that the angle β made by the forward or cutting stroke is greater than the angle α described by
the return stroke. Since the crank rotates with uniform angular speed, therefore the return stroke is completed within
shorter time. Thus it is called quick return motion mechanism.

5. Whitworth quick return motion mechanism.
This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD (link 2)
forming the turning pair is fixed, as shown in Fig. The link 2 corresponds to a crank in a reciprocating
steam engine. The driving crank CA (link 3) rotates at a uniform angular speed. The slider (link 4)
attached to the crank pin at A slides along the slotted bar PA (link 1) which oscillates at a pivoted point D.
The connecting rod PR carries the ram at R to which a cutting tool is fixed. The motion of the tool is
constrained along the line RD produced, i.e. along a line passing through D and perpendicular to CD.
Fig. Whitworth quick return motion mechanism.

When the driving crank CA moves from the position CA1 to CA2 (or the link DP from the
position DP1 to DP2) through an angle α in the clockwise direction, the tool moves from the left hand end
of its stroke to the right hand end through a distance 2 PD.
Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 to DP1 )
through an angle β in the clockwise direction, the tool moves back from right hand end of its stroke to the
left hand end.
A little consideration will show that the time taken during the left to right movement of the ram (i.e. during
forward or cutting stroke) will be equal to the time taken by the driving crank to move from CA1 to CA2.
Similarly, the time taken during the right to left movement of the ram (or during the idle or return stroke)
will be equal to the time taken by the driving crank to move from CA2 to CA1.
Since the crank link CA rotates at uniform angular velocity therefore time taken during the cutting stroke
(or forward stroke) is more than the time taken during the return stroke. In other words, the mean speed of
the ram during cutting stroke is less than the mean speed during the return stroke.
The ratio between the time taken during the cutting and return strokes is given by
Note. In order to find the length of effective stroke R1 R2, mark P1 R1 = P2 R2 = PR. The length of effective
stroke is also equal to 2 PD.

Double Slider Crank Chain
A kinematic chain which consists of two turning pairs and two sliding pairs is known as double slider crank
chain, as shown in Fig. We see that the link 2 and link 1 form one turning pair and link 2 and link 3 form
the second turning pair. The link 3 and link 4 form one sliding pair and link 1 and link 4 form the second
sliding pair. Inversions of Double Slider Crank Chain
1.Elliptical trammels. It is an instrument used for drawing ellipses. This inversion is obtained by
fixing the slotted plate (link 4), as shown in Fig.
The fixed plate or link 4 has two straight grooves cut in it, at right angles to each other. The link 1 and link
3, are known as sliders and form sliding pairs with link 4. The link AB (link 2) is a bar which forms turning
pair with links 1 and 3. When the links 1 and 3 slide along their respective grooves, any point on the link 2
such as P traces out an ellipse on the surface of link 4, as shown in Fig. (a). A little consideration will show
that AP and BP are the semi-major axis and semi-minor axis of the ellipse respectively. This can be proved
as follows :
Let us take OX and OY as horizontal and vertical axes and let the link BA is inclined at an angle θ with the
horizontal, as shown in Fig. (b). Now the co-ordinates of the point P on the link BA will be
x = PQ = AP cos θ; and y = PR = BP sin θ

Fig. Elliptical trammels.
This is the equation of an ellipse. Hence
the path traced by point P is an ellipse
whose semi-major axis is AP and semi-
minor axis is BP.
Note : If P is the mid-point of link BA,
then AP = BP. The above equation can
be written as
This is the equation of a circle whose radius is AP. Hence
if P is the mid-point of link BA, it will trace a circle.
2. Scotch yoke mechanism.
This mechanism is used for converting rotary motion into
a reciprocating motion. The inversion is obtained by
fixing either the link 1 or link 3. In Fig., link 1 is fixed.
In this mechanism, when the link 2 (which corresponds to
crank) rotates about B as centre, the link 4 (which
corresponds to a frame) reciprocates. The fixed link 1
guides the frame.
Fig. Scotch yoke mechanism.

3. Oldham’s coupling.
An Oldham's coupling is used for connecting two parallel shafts whose axes are at a small distance apart.
The shafts are coupled in such a way that if one shaft rotates, the other shaft also rotates at the same speed.
This inversion is obtained by fixing the link 2, as shown in Fig. (a). The shafts to be connected have two
flanges (link 1 and link 3) rigidly fastened at their ends by forging. The link 1 and link 3 form turning pairs
with link 2. These flanges have diametrical slots cut in their inner faces, as shown in Fig. (b).
The intermediate piece (link 4) which is a circular disc, have two tongues (i.e. diametrical projections) T1
and T2 on each face at right angles to each other, as shown in Fig. (c).
Fig: Oldham’s coupling.

The tongues on the link 4 closely fit into the slots in the two flanges (link 1 and link 3). The link 4 can slide
or reciprocate in the slots in the flanges. When the driving shaft A is rotated, the flange C (link 1) causes
the intermediate piece (link 4) to rotate at the same angle through which the flange has rotated, and it
further rotates the flange D (link 3) at the same angle and thus the shaft B rotates. Hence links 1, 3 and 4
have the same angular velocity at every instant. A little consideration will show, that there is a sliding
motion between the link 4 and each of the other links 1 and 3. If the distance between the axes of the shafts
is constant, the centre of intermediate piece will describe a circle of radius equal to the distance between
the axes of the two shafts.
Therefore, the maximum sliding speed of each tongue along its slot is equal to the peripheral velocity of the
centre of the disc along its circular path.
Let ω = Angular velocity of each shaft in rad/s, and
r = Distance between the axes of the shafts in metres.
∴ Maximum sliding speed of each tongue (in m/s),
v = ω.r

Intermittent Motion Mechanisms
Intermittent motion means that the motion is not continuous but it is ceased at definite intervals.
Ratchet and Pawl Mechanism
This mechanism is used in producing intermittent rotary motion from an oscillating or reciprocating motion
member. A ratchet and Pawl mechanism consists of a ratchet wheel 2 and a Pawl 3 as shown in fig. when
the lever 4 carrying Pawl is raised, the ratchet wheel rotates in CCW direction (driven by Pawl).
As the pawl lever is lowered the Pawl slides over the ratchet teeth. One more Pawl 5 is used to prevent the
ratchet from reversing. Ratchets are used in feed mechanisms, lifting jacks, clocks, watches and counting
device.
Fig: Ratchet and Pawl Mechanism

GENEVA MECHANISM: Geneva is one more intermittent
mechanism. Consists of driving wheel with a pin which engages
slot of the follower. During quarter revolution of the driving plate
the pin and the follower remain in contact and hence follower is
turned by quarter turn and follower remains rest during remaining
time of the driving wheel. This particular mechanism used in
preventing over winding of main spring in clocks. To avoid shock
the pin movement should be tangential to the follower and driving
wheel. Fig: GENEVA MECHANISM
PEAUCELLIER MECHANISM: The pin A constrained to move along
the circumference of circle by means of link OA. OP is fixed link, and
OA and OP has same length. A and C are opposite corners of a 4 bar
mechanism with links AB, BC, CD and DA of equal length. Pins B and D
are connected by links of equal lengths from fixed point P. It can be
proved that the product of PB and PD remains constant there fore point
C traces straight line normal to PE.
Fig: PEAUCELLIER MECHANISM

TOGGLE MECHANISM: In slider crank mechanism as crank
approaches one of its dead center position the slider approaches zero.
The ratio of crank movement and slider movement approaching infinity
is proportional to the mechanical advantage. This is the main principle
used in toggle mechanism. When large amount of force need to act over
a small distance.
P*tanα=(F/2)
P= F/(2*tanα)
Thus for a given value of F bottom links approaches collinear position (i.e.
α→0), the force P rises rapidly (i.e. P →∞). This mechanism is used in punch
presses, stone crushers etc.
Fig: TOGGLE MECHANISM
PANTOGRAPH: This mechanism is used in copying devices since it gives reduced or
enlarged scale drawings. It is also used as guiding of cutting tool.
All the links are pin joined here and mathematically it can proved that point traced by B
is similar to point traced by A and vice-versa.
The same mechanism is used in guiding a cutting tool if you move guider by small
distance in the same way in the same direction the actual cutting tool will move by a
large distance.
Fig: PANTOGRAPH

STEERING MECHANISMS:
The relative motion between the road and the wheels are pure rolling. In order to maintain the rolling when
vehicle is taking turn, the steering gears must be designed that the paths of points of contact of each wheel
with the ground are concentric circular arcs. Steering is usually effected by turning the axes of rotation of
the two front wheels relative to the chassis of the vehicle, and to satisfy the above condition, the axis of the
wheel on the inside of the curve must be turned through a larger angle than the axis of the wheel on the
outside of the curve. The front wheels are mounted on short separate axles which are pivoted to the chassis
of the car. Fig shows the plan view in which AB and CD are the two axles with pivots at A and C. when
turning to the right the axes AB and CD intersect the common axis EF of the rear wheels at the point G, so
that the path of contact of each wheel with the ground is circular are with centre G. While taking turns ,the
condition of perfect rolling is satisfied if the axes of the front wheels when produced meet the rear wheel axis at
one point. Then this point is the instantaneous centre of the vehicle.
AC=EF=EG-FG
tanӨ=(CF/FG)
FG=(CF/ tanӨ)=CF*cotӨ
tanФ=(AE/EG)
EG=(AE/ tanФ)=AE*cotФ
AC= AE*cotФ- CF*cotӨ
cotФ- cotӨ=(AC/AE)=(a/w)

Fig: ACKERMANN STEERING MECHANISM
This mechanism is made on only turning
pairs and is based on 4–bar chain
mechanism. Since it h as only turning pairs
wear and tear of parts is less and is cheaper
in manufacturing. Cross link KL is
connected between two short axles AC and
BD of the front wheels, it form bell crank
levers CAK and DBL. ABLK forms a 4-
bar chain mechanism.
When the vehicle is moving in straight line link AB and KL are parallel and short links AK and BL are inclined at an
angle of “α” . When vehicle takes right turn link BL turned to increase ‘α’, where as the long link LK causes other
short link AK to turn so as to reduce ‘α’ .
The fundamental equation for correct steering mechanism is
From the above equation it is clear that the angle Ф through which AK turns is less than the angle Ө through which
BL turns and therefore the left front axle turns through a smaller angle than the right front axle.
For different angles of Ө, corresponding angles Ф are noted down. This is done by actually drawing the mechanism to
a scale or by calculation. Therefore for different values of Ө the corresponding values of Ф and cotФ- cotӨ are
tabulated. Approximate value of (b/l) for correct steering should be 0.4-0.5. here instantaneous center doesn’t lie on
the axis of rear axle but on a line parallel(above) to the rear axles at a distance of 0.3l.
cotФ- cotӨ=(AB/AE)=(b/l)
ACKERMANN STEERING MECHANISM

Correct steering positions:
(i) When moving straight,
(ii) When moving at one correct angle to the right corresponding to link ratio AK/AB and angle ‘α’,
(iii) Similar position when moving to the left.
DAVIS STEERING MECHANISM
Davis steering gear is an exact steering gear mechanism. It has two sliding pairs and two turning pairs. In this
mechanism, the slotted links are attached to the front wheel axle, which turn about two pivotal points. It has the rod
and it is constrained to move in the direction of its length by the sliding two members. These constraints are
connected to the slotted link by a sliding and a turning pair at each end. The main drawback in Davis steering
mechanism is wear and tear problem of sliding pairs. The drawbacks in Davis steering mechanism are overcome by
Ackermann steering gear mechanism. Davis mechanism is mathematically perfect mechanism.

It consists of a cross link CD sliding parallel to another link AB and is connected to stub axles of the two front wheels
by two bell crank levers LAC and MBD pivoted at A and B respectively.
The cross link CD slides in the bearing and carries pairs at its ends C and D.
The slide blocks are pivoted on these pins and move with turning bell crank levers as the steering wheel operated.
When the wheel is running straight, the gear is said to be in mid position.
The short arms AC and BD are inclined at an angle (90ͦ+α) to their stub axle AL and BM, respectively.
The correct steering depends upon the suitable selection of cross-arm angle α, which is given by
tan α=(c/2*b)
Where, c= Distance between the pivots of front axles,
b=Wheel base
The range of (c/b) is 0.4 to 0.5 and hence α lies between 11.3ͦ to 14.1ͦ

Kinematics of Machinery

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