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Mechanical spider ( GQ64)

INTRODUCTION

GQ64 is not a robotics-based machine. It is the simplest form of mechanism which runs with the help of mechanisms like

gear drive
belt drive
motor drive
chain and sprocket drive

The walking mechanism has been for long a dynamic and fast-developing field of mechatronics. This huge interest not only derives from the obvious fact that the usage of legs resembles the way of movement of living animals, but also to its great advantage while moving on a rough, unstructured surface. Due to the possibility to stand on single, well-defined points, a flexible operation area is achieved.

As a drawback, efficiency and speed are not the strongest qualities of a walking mechanism. When it comes to flat, even terrain, moving with wheels turns out to be the faster, more reliable way of locomotion.

The invention provides a walking device that stimulates a gait of a legged animal. The device includes a frame with spaced axial mounts, a leg, axially connected upper and lower rocker arms which limit reciprocating leg motion. The leg is driven by a connecting arm powered by a rotating crank. The position and configuration of the axial connecting sites establish a prescribed orbital path that the foot undertakes with
each revolution of the crank. Both rocker arms and the crank are axially mounted to the frame.
The leg has a hip joint axially connected to the upper rocker arm for limiting hip motion, a foot and a knee joint axially connected to the connecting arm. The connecting arm has three axial connecting sites, one for connecting to the knee, another to the crank, and a third connecting site defined as a centrally disposed elbow joint connecting site which connects onto the lower rocker arm and limits knee joint motion. Under power, crank rotation is transferred to the connecting arm causing the leg to move in an accurate reciprocating movement of a restricted actual pathway which stimulates the gait of the legged animal. The walking device may be manually powered or motorized by applying motorized power to the crank axles.

Klann mechanism is a planar mechanism designed to simulate the giant legged animal and function as a wheel replacement. Here we are using a single leg consisting of a six–bar linkage made up entirely of pivot joint that converts rotating motion into linear motion. The linkage consists of the frame, a crank, two grounded rockers, and two couplers all connected by pivot joints. The proportions of each of the links in the mechanism are defined to optimize the linearity of the foot for one-half of the rotation of the crank.

The remaining rotation of the crank allows the foot to be raised to a predetermined height before returning to the starting position and repeating the cycle. Two of these linkages coupled together at the crank and one-half cycle out of phase with each other will allow the frame of a vehicle to travel parallel to the ground. The Klann linkage provides many of the benefits of more advanced walking vehicles without some of their limitations. It can step over curbs, climb stairs, or travel into an area that are currently not accessible with wheels but does not require microprocessor control or multitudes of actuator mechanisms.

WHAT IS GQ64?

G – General

Q – Quadric System

6 – Six Links

4 – Four Legs

MECHANISMS USED

Technical Mechanism

Klann mechanistic mechanism

BIOLOGICAL MECHANISM

ANATOMY F A SPIDER

Most insects have three body parts. Spiders and other arachnids have only two major body parts. The anterior part is called the cephalothorax or prosoma, and the posterior part is called the abdomen, or opisthosoma.

Spiders have eight legs attached to the cephalothorax and each pair of legs is numbered I, II, III and IV from anterior to posterior. Each leg is composed out of seven segments: coxa or basal segment, the trochanter, femur, patella, tibia, metatarsus and tarsus.

In some spider families, the tarsus ends in two claws, in others it ends in three claws, depending on the adaptation to the environment and hunting technique.

The front appendages are called pedipalps and have only six segments: coxa, trochanter, femur, patella, tibia and tarsus. Different types of hairs (setae) and spines (macrosetae) are present on the legs. Also, long hairs are present called trichobothria and these hairs are used as sensory

units and they originate in sockets with multiple nerve endings. These hairs are extremely sensitive to air currents and to vibrations, compensating for the extremely poor eye sight of some spiders thus helping them hunt. Different types of hairs and bristles are found on the legs, depending on the different taxa, as an adaptation to the environment and climbing or hunting techniques.

For example, the spiders in the family Theridiidae are called “comb-footed spiders” because of the appearance of the bristles that they have on the ventral side of the tarsus.

The spider’s body does not have veins or arteries to conduct the blood, a liquid called haemolymph runs through the open spaces in the body.

The spider does not use muscles to pull tendons and actuate the legs, instead the prosoma pumps pressurized fluid into chambers into the joints of the legs, and these chambers expand causing the angle between the two-leg segments to modify, though having the same effect that a tendon being pulled would have. Studying the way that spiders use their legs to move forward it is possible to say that the 2 anterior legs are used to pull in towards the body while climbing, 2 pairs of lateral legs who travel upwards and then pull in and laterally while climbing and the last pair is placed at the rear and used for climbing balance and pushing. These considerations are only true for spiders capable to climb.

Because of the variety of environments where spiders live (on the water, under the water,caves, trees,on the ground) there is a very large number of spider species with very different adaptations to environment.

With these different adaptations arthropods walk over demanding terrain much more effectively than any existing autonomous robot. Spiders use distributed neutral feedback for precise stepping in order to deal with unstructured environments

EXPERIMENTAL EVIDENCES

In order to be able to climb various surfaces the spiders use two types of different attaching mechanisms: the claws and the hairs.

As regards as the claws such a mechanisms are used for two major operations:

• locomotion, used during climbing rough hard surfaces (stone) or soft surfaces (tree bark, leaves)

• web building, used to spin the silk threads or walk on the already built web.

Web building spiders have three claws and use the claw in the middle to grasp the silk threads. Jumping spiders and generally spiders that do not use webs to capture the prey do not need specialized claws to spin the silk threads

TRANSMITTING SYSTEM

Which type of system you need to provide the power into legs for translation motion , in this system crank are the most common part because the main power are transmitted in crank , crank rotates with his own center the leg are joint with the help of pivot .

Main type of transmitting

Mechanical spider with gear mechanism
Mechanical spider without gear

MOTIVATION

To overcome the previously mentioned problematic a practical solution would be to enable different ways of travelling for one robot, rolling and walking, to adapt it to a changing environment in an easy way. In this bachelor thesis this task is realized by implementing feet equipped with passive skates on a walking robot, deriving a skating trajectory and do first steps into optimization of this movement. One of the main reasons for this choice was that the robot stays in the environment it is geared to. Therefore not the whole robot, but only the feet had to be altered.

BASIC STUDY ABOUT MECHANISM

PLANAR, SPHERICAL AD SPATIAL MECHANISMS

Mechanisms may be categorized in several different ways to emphasize their similarities and differences. One such grouping divides mechanisms into planar, spherical and spatial categories.

A planar mechanism is one in which all particles describe plane curves in space and all these curves in space and all these curves lie in parallel planes; i.e., the loci of all points are plane curves parallel to a single common plane. This characteristic makes it possible to represent the locus of any chosen point of a planar mechanism in its true size and shape on a single drawing. The motion transformation of any such mechanism is called coplanar. The vast majority of mechanisms in use today are coplanar.

Planar mechanisms utilizing only lower pairs are called planar linkages; they may include only revolute and prismatic pairs. Although a planar pair might theoretically be included, this would impose no constraint and thus be equivalent to an opening in the kinematic chain. Planar motion also requires that the axes of all prismatic pairs and all revolute axes be normal to the plane of motion.

A spherical mechanism is one in which each link has some point which remains stationary as the linkage moves and in which the stationary points of all links lie at a common location, i.e., the locus of each point is a curve contained in a spherical surface, and the spherical surfaces defined by several arbitrary chosen points are all concentric. The motions of all particles can therefore be completely described by their radial projections, or “shadows” on the surface of a sphere with properly chosen center. Hook’s universal joint is perhaps the best example of spherical mechanism.

Spherical linkages are constituted entirely of revolute pairs. A spheric pair would produce no additional constraints and would thus be equivalent to an opening in chain, while all other lower pairs have nonshperic motion. In spheric linkages, the axes of all revolute pairs must intersect at a point.

Spatial mechanism, on the other hand, includes no restrictions on the relative motions of the particles. The motion of the particles. The motion transformation in not necessarily coplanar, nor must it be concentric. A spatial mechanism may have particles with loci of double curvature. Any linkage which contains a screw pair.

Thus, the overwhelmingly large category of planar mechanisms and the category of planar mechanisms and the category of spherical mechanisms are only special cases, or subsets, of the all-inclusive category spatial mechanisms. They occur as a consequence of special geometry in the particular orientations of their axes.

If planar and spherical mechanisms are only special cases of spatial mechanisms. Why is it desirable to identify them separately? Because of the particular geometric conditions which identify these types, many simplifications are possible in their design and analysis. As pointed out earlier, it is possible to observe the motions of all particles of a planar mechanism in true size and shape from a single direction. In other words, all motions can be represented graphically in a single view. Thus, graphical techniques are well suited to their solution. Since spatial mechanisms do not all have this fortunate geometry, visualization becomes more difficult and more powerful techniques must be developed for their analysis.

Since the vast majority of mechanisms in use today are planar, one might question the need of the more complicated mathematical techniques used for spatial mechanisms .There are a number of reasons why more powerful methods are value though the simpler graphical techniques have been mastered.

They provide new, alternative methods which will solve the problems in a different way .Thus they provide a means of checking results. Certain problems by their nature may also be more amenable to one method than another.
Methods which are analytical in nature are better suited to solution by calculator or digital computer than graphical techniques.
Even though the majority of useful mechanisms are planar and well suited to graphical solution, the few remaining must also be analyzed, and techniques should be known for analyzing them.
One reason that planar linkages are so common is that good methods of analysis for the more general spatial linkages have not been available until quite recently. Without methods for their analysis, heir design and use has not been common, even though they may be inherently better suited in certain applications.
We will discover that spatial linkages are much more common in practice than their formal description indicates.

According to the relative motion of the rigid bodies. In planar mechanisms, all of the relative motions of the rigid bodies are in one plane or in parallel planes. If there is any relative motion that is not in the same plane or in parallel planes, the mechanism is called the spatial mechanism. In other words, planar mechanisms are essentially two dimensional while spatial mechanisms are three dimensional.

When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriter etc,

A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism. When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine. In such cases, the various links or elements have to be designed to withstand the forces (both static and kinetic) safely.

NUMBER OF DEGREES OF FREEDON FOR PLANAR MECHANISM

In the design or analysis of a mechanism, one of the most important concerns is the number of degrees of freedom (also called movability) of the mechanism. It is defined as the number of input parameters (usually pair variables) which must be independently controlled in order to bring the mechanism into a useful engineering purpose. It is possible to determine the number of degrees of freedom of a mechanism directly from the number of links and the number and types of joints which includes.

Now let us consider a plane mechanism with ‘l’ number of links.

Since in a mechanism, one of the links is to be fixed, therefore the number

of movable links will be ‘(l – 1)’ and thus the total number of degrees of

Freedom will be ‘3 (l – 1)’ before they are connected to any other link. In

General, a mechanism with ‘l’ number of links connected by ‘j’ number of

Binary joints or lower pairs (i.e. single degree of freedom pairs) and ‘h’

Number of higher pairs (i.e. two degree of freedom pairs), then the

Number of degrees of freedom of a mechanism is given by-

n = 3 (l – 1) – 2 j – h

Kutzbach Criterion to Plane Mechanisms

n = 3 (l – 1) – 2 j – h

Grubler’s Criterion for Plane Mechanisms

The Grubler’s criterion applies to mechanisms with only single degree of freedom joints.
Where the overall movability of the mechanism is unity. Substituting n = 1 and h = 0 in Kutzbach equation, we have
1 = 3 (l – 1) – 2 j
or

3l – 2j – 4 = 0

This equation is known as the Grubler’s criterion for plane mechanisms with constrained motion. A little consideration will show that a plane mechanism with a movability of 1 and only single degree of freedom joints cannot have odd number of links. The simplest possible machanisms.of this type are a four bar mechanism and a slider-crank mechanism in which l = 4 and j = 3.2 Kinematics and Dynamics of Mechanisms.

KINEMATICS, KINETICS, DYNAMICS

Kinematics of mechanisms is concerned with the motion of the parts without considering how the influencing factors (force and mass) affect the motion. Therefore, kinematics deals with the fundamental concepts of space and time and the quantities velocity and acceleration derived there from.

Kinetics deals with action of forces on bodies. This is where the effects of gravity come into play.

Dynamics is the combination of kinematics and kinetics. Dynamics of mechanisms concerns the forces that act on the parts — both balanced and unbalanced forces, taking into account the masses and accelerations of the parts as well as the external forces.

MACHINE

Machine is a device which receives energy and transforms it into some useful work. A machine consists of a number of parts or bodies.

KINEMATIC LINK OR ELEMENT

Each part of a machine, which moves relative to some other part, is known as a kinematic link ( or simply link) or element. A link may consist of several parts, which are rigidly fastened together, so that they do not move relative to one another.

For example, in a reciprocating steam engine, piston, piston rod and crosshead constitute one link; connecting rod with big and small end bearings constitute a second link; crank, crank shaft and flywheel a third link and the cylinder, engine frame and main bearings a fourth link A link or element need not to be a rigid body, but it must be a resistant body. A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation. Thus a link should have the following two characteristics:

1. It should have relative motion, and

2. It must be a resistant body

TYPES OF LINKS

In order to transmit motion, the driver and the follower may be connected by the following three types of links:

1. Rigid link.

A rigid link is one which does not undergo any deformation while transmitting motion. Strictly speaking, rigid links do not exist. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable; they can be considered as rigid links.

2. Flexible link.

A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. For example, belts, ropes, chains and wires are flexible links and transmit tensile forces only.

3. Fluid link.

A fluid link is one which is formed by having a fluid in a receptacle and the motion is transmitted through the fluid by pressure or compression only, as in the case of hydraulic presses, jacks and brakes.

STRUCTURE

It is an assemblage of a number of resistant bodies (known as members) having no relative

Motion between them and meant for carrying loads having straining action. A railway bridge, a roof

Truss, machine frames etc., are the examples of a structure.

KINEMATIC PAIR

The two links or elements of a machine, when in contact with each other, are said to form a Pair. If the relative motion between them is completely or successfully constrained (i.e. in a definite Direction), the pair is known as kinematic pair

TYPES OF CONSTRAINED MOTION

Following are the three types of constrained motions:

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. For example, the piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction (i.e.it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank The motion of a square bar in a square hole, as shown in Fig. 5.2, and the motion of a shaft with collars at each end in a circular hole, are also examples of completely constrained motion.

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. A circular bar or shaft in a circular hole, is an example of an incompletely constrained motion as it may either rotate or slide in a hole. These both motions have no relationship with the other.

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. Consider a shaft in a foot-step bearing. The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely constrained motion. But if the load is placed on the shaft to prevent axial upward movement of the shaft, then the motion of the pair is said to be successfully constrained motion.

CLASSIFICATION OF KINEMATIC PAIR

The kinematic pairs may be classified according to the following considerations:

According to the type of relative motion between the elements.

The kinematic pairs according to type of relative motion between the elements may be classified as discussed below:

Sliding pair.

When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair. The piston and cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed etc. are the examples of a sliding pair. A little consideration will show that a sliding pair has a completely constrained motion.

Turning pair.

When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is known as turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in head stock, cycle wheels turning over their axles etc. are the examples of a turning pair. A turning pair also has a completely constrained motion.

Rolling pair.

When the two elements of a pair are connected in such a way that one roll over another fixed link, the pair is known as rolling pair. Ball and roller bearings are examples of rolling pair.

Screw pair.

When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut, and bolt with a nut are examples of a screw pair.

Spherical pair.

When the two elements of a pair are connected in such a way that one element (with spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand etc., are the examples of a spherical pair.

According to the type of contact between the elements.

The kinematic pairs according to the type of contact between the elements may be classified as discussed below:

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.

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. A pair of friction discs, toothed gearing, belt and rope drives ,ball and roller bearings and cam and follower are the examples of higher pairs.

According to the type of closure.

The kinematic pairs according to the type of closure between the elements may be classified as discussed below:

Self closed pair.

When the two elements of a pair are connected together mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair.

Force – closed pair.

When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity.

KINEMATIC CHAIN

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion); it is called a kinematic chain. In other words, a kinematic chain may be defined as a combination of kinematic pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained. For example, the crankshaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourth pair. The total combination of these links is a kinematic chain.

If each link is assumed to form two pairs with two adjacent links, then the relation between the number of pairs (p) forming a kinematic chain and the number of links (l) may be expressed in the form of an equation:

l= 2p 4 . . . (I)

Since in a kinematic chain each link forms a part of two pairs, therefore there will be as many links as the number of pairs. Another relation between the number of links (l) and the number of joints (j) which

Constitute a kinematic chain is given by the expression:

j=3/2l–2 . . . (ii)

The equations (i) and (ii) are applicable only to kinematic chains, in which lower pairs are used. These equations may also be applied to kinematic chains, in which higher pairs are used. In that case each higher pair may be taken as equivalent to two lower pairs with an additional element or link.

TYPES OF JOINTS IN A CHAIN

The following types of joints are usually found in a chain:

Binary joint.

When two links are joined at the same connection, the joint is known as binary joint. For example, a chain as shown in Fig. 5.10, has four links and four binary joins at A, B,C and D. In order to determine the nature of chain, i.e. whether the chain is a locked chain (or structure) or kinematic chain or unconstrained chain, the following relation between the number of links and the number of binary joints, as given by A.W. Klein, may be used:

j+h/2=3/2l-2

Where,

j= Number of binary joints,

h= Number of higher pairs, and

l= Number of links.

When h= 0, the equation (i), may be written as

J=3/2l-2

Ternary joint.

When three links are joined at the same connection, the joint is known as ternary joint. It is equivalent to two binary joints as one of the three links joined carry the pin for the other two links. For example, has six links. It has three binary joints at A, B and Dand two ternary joints at Cand E. Since one ternary joint is equivalent to two binary joints, therefore equivalent binary joints in a chain.

Quaternary joint.

When four links are joined at the same connection, the joint is called a quaternary joint. It is equivalent to three binary joints. In general, when lnumber of links are joined at the same connection, the joint is equivalent to (l– 1) binary joints.

MECHANISM

When one of the links of a kinematic chain is fixed, the chain is known as mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriter etc. A mechanism with four links is known as simple mechanism, and the mechanism with more than four links is known as compound mechanism. When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine. In such cases, the various links or elements have to be designed to withstand the forces (both static and kinetic) safely.

INVERSION OF A MECHANISM

We have already discussed that when one of links 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.

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.

FOUR BAR CHAIN OR QUADRIC CHAIN

We have already discussed that the kinematic chain is a combination of four or more kinematic pairs, such that the relative motion between the links or elements is completely constrained. The simplest and the basic kinematic chain is a four bar chain or quadric cycle chain, as shown in. It consists of four links, each of them forms a turning pair at A, B, C and D. The four links may be of different lengths. According to Grashof ’s law for a four bar mechanism, the sum of the shortest and longest link lengths should not be greater than the sum of the remaining two link lengths if there is to be continuous relative motion between the two links. A very important consideration in designing a mechanism is to ensure that the input crank makes a complete revolution relative to the other links. The mechanism in which no link makes a complete revolution will not be useful. In a four bar chain, one of the links, in particular the shortest link, will make a complete revolution relative to the other three links, if it satisfies the Grashof’s law. Such a link is known as crank or driver. AD (link 4) is a crank. The link BC(link 2) which makes a partial rotation or oscillates is known as lever or rocker or follower and the link CD(link 3) which connects the crank and lever is called connecting rod or coupler .The fixed link AB(link 1) is known as frame of the mechanism. When the crank (link 4) is the driver, the mechanism is transforming rotary motion into oscillating motion.

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. 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.

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. 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.

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. The four links are: fixed link at A, link AC, link CE and link BFD. 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 Eat the end of the link CE traces out approximately a straight line.

SINGLE SLIDER CRANK CHAIN

A single slider crank chain is a modification of the basic four bar chain. It consists 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, 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.

Inversions of Single Slider Crank Chain

Pendulum pump or Bull engine.

In this mechanism, the inversion is obtained by fixing the cylinder or link 4 (i.e. sliding pair). 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 has two pistons attached to link 1.

2. Oscillating cylinder engine.

The arrangement of oscillating cylinder engine mechanism. It 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.

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 D, 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.

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. 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.

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. 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 Rto 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.

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. 5.34. 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

Elliptical trammels.

It is an instrument used for drawing ellipses. This inversion is obtained by fixing the slotted plate (link 4). 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.

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. Link 1 is fixed. In this mechanism, when the link 2 (which corresponds to crank) rotates aboutBas centre, the link 4 (which corresponds to a frame) reciprocates. The fixed link 1 guides the frame.

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. The shafts to be connected have two flanges (link 1 and link 3) rigidly fastened at their ends by forging.

Concept Determination

Several concepts for feet giving the robot the opportunity to reach new environ-ments or studying new locomotion concepts were in mind. After reconsidering the potential of different approaches their number could be reduced to the following promising options

A single leg consists of a six-bar linkage made up entirely of pivot joints that converts rotating motion into linear motion. One hundred and eighty degrees of the input crank results in the straight-line portion of the path traced by the foot. The result of two of these linkages coupled together at the crank and one-half cycle out of phase with each other is a device that can replace a wheel and allow the frame of the vehicle to travel relatively parallel to the ground. The remaining rotation of the input crank allows the foot to be raised to a predetermined height before returning to the starting position and repeating the cycle.

These figures show a single linkage in the fully extended, mid-stride, retracted, and lifted positions of the walking cycle. These four figures show the crank (rightmost link in the first figure on the left with the extended pin) in the 0, 90, 180, and 270 degree positions.

SKATING

In this concept the robot travels a flat, unstructured surface by skating. Each leg should be equipped with passive wheels on the feet. By moving the feet in specific way thrust is induced. Designing the specialized feet and deriving a possible trajectory are the emphases of this approach. The goal would be to move faster on the floor than with legged locomotion

Selected Method of Skating, why???

It was decided to further pursuit this way of movement for a couple of reasons:First of all with eight legs on the floor a very stable system is attained. Furthermore, lifting the legs would lead to a dislocation of the robots center of mass.

That means dynamic calculations have to be applied leading to a more complex problem. Aside from that, feet equipped with skating rolls turned out to be quite heavy. When lifted up, high torques in the joints would be generated. That way the motors could be overloaded.

KLANN MECHANISTIC MECHANISM

This mechanism is based on simple kinematic chain, and kinematic chain based on links joint and pivots.

The study of Biological systems and methods has long intrigued Scientists and Engineers in their quest for a greater understanding of the world. Biological systems have managed over thousands of years to evolve many methods for completing tasks that are naturally impossible for humans such as re-growing missing limbs, breathing underwater and even flying. Although humans have managed to mimic some of these abilities through the inventions of submarines and airplanes, there are still many areas of engineering that these biological marvels can be applied to. Biometics, the study of Biological methods and systems and their implications toward robotic systems and engineering problems, is the term applied to this ancient art, and has gained prominence in recent years for its novel solutions.

MOTION- (pictorial representation)

The Klann linkage provides many of the benefits of more advanced walking vehicles without some of their limitations. It can step over curbs, climb stairs, or travel into areas that are currently not accessible with wheels but do not require microprocessor control or multitudes of inefficient actuator mechanisms. It fits into the technological void between these walking devices and axel-driven wheels.

FINIAL MECHNISM-

SYSTEM OVERVIEW

The basic function of the GQ64 o move in a coordinated manner. Much like realspiders, the gq64uld be designed to facilitate vertical motion. The most commonsolution to this requirement is making the design both lightweight and by using an adhesive

Substance on the feet.

The important functional requirements are listed below:

Fur legs( KLENN MECHANISM )
Three degrees of freedom on each leg
Lightweight
Coordinated Movement in forward direction
Ability to stick to surfaces

RANGE OF MOTION

The range of motion (ROM) describes all positions the foot can be moved to. It is derived from length of the leg elements and obtainable angles between the segments. Furthermore, it had to be guaranteed that the wheels stay in contact to the ground at all times. With the geometry of the skating device and a security factor to avoid the wheel suspension touching the ground a minimal radius of 110 mm and a maximal radius of 410 mm was determined. For these values are independent from the chosen α angle, the range of motion emerges as an annular area with the shoulder as a center The minimum and maximum angle are defined by the bulges of the body panel and therefore diver from leg to leg. For the leg L2 and R2 which were chosen to carry out the skating movement, the α angle ranges from the minimum of 94 to the maximum of 46 degrees.

RESTRICTIVE FACTORS

Until now, attention was only paid to an ideal case, which strongly simplifies the reality. Since the thesis is based on a real robot, the restrictive factors of the system itself and of its interaction with a test environment had to be taken into account.

THE EQUILIBRIUM LINE

The equilibrium line describes the set of all positions in which the orientation of the skate is parallel to the driving direction. This is the case if the currentα angle has the same value as the γ angle of the leg. These positions generate one defined line going through the center of the

Shoulder and the standard position of the foot.

The great importance of this line can be explained by observing the behavior of a skate positioned once exactly on the line and once on the left respective the right of it with a constant velocity of the shoulder.

Starting with the first case: By placing the wheel on the equilibrium line, a stable state is obtained. To maintain the velocity of the shoulder, the skate can stay passively on this position. To avoid this deadlock position, the skate has to be pushed artificially over the line. This is only possible in x-direction, since the skate constraint blocks the y-direction. If the skate is now placed on the left of the equilibrium line, a given velocity in the shoulder requires a relative movement in positive y-direction such the skate has to move along the rolling direction. Respective, placed on the right side, the skate has to carry out a motion in negative y-direction . The movement in positive respective negative y-direction is depending on the total angular deflection measured from the equilibrium line, the so called deflection angle. The bigger the absolute value of this parameter becomes, the stronger is the tendency to move in y-direction. Based on the previous considerations to accomplish a closed movement, the trajectory has to be positioned around the equilibrium line. A possible solution is a Circular shaped trajectory that has to be travelled clockwise on the left side And anticlockwise on the right side of the machine.

MECHANICAL DESIGN OF SKATES

Requirements

For the feet with integrated skating wheels, the following characteristics are required: First of all, the feet have to be compatible with the plug connection of the robot. Second, a skating roll with high friction has to be integrated. Furthermore, the rolling direction has to be adjusted for each leg to have all rolls directed forward in the standard position

Results of the Sector Approach

For particular selection of the actuating variables blurred trajectories could be determined.

As it can be seen in the movement of the skate stabilizes on the same area for different starting positions of the skate. The main difference between the behaviors of the skate for different starting positions is the duration till the movement is leveled off at the stable area. This conclusion is only valid as long as the starting point is close to the equilibrium line, since for remote staring points the motion turns out to be unstable.

APPLICATIONS

Potential applications would include anything that currently uses wheels. The possibilities are limited only by the imagination.
Proposed concepts such as the ones reported on regarding remote media reporters or various military land drones could be improved with this linkage.

Further development could result in a production version of a wheelchair that could handle curbs, sand, gravel, and stairs. Making the world of someone confined to a wheel chair a much bigger place.

The military, law enforcement, Explosive Ordinance Disposal units, and private security firms could also benefit from applications of the spider bike. It would perform very well as a platform with the ability to handle stairs and other obstacles to wheeled or tracked vehicles. Unmanned operations could be used for reconnaissance, patrolling, hazardous material handling, clearing minefields, or secure an area without putting anyone at risk. There would be further benefits if a portion of these tasks could be automated or made more accurate through Global Positioning Systems, infrared viewing, and audio and video recording. It could be programmed to patrol a predefined perimeter at random intervals.

It would be difficult to compete with the efficiency of a wheel on smooth hard surfaces but as condition increases rolling friction, this linkage becomes more viable and wheels of similar size cannot handle obstacles that this linkage is capable of. Toys could be developed that would fit in the palm of your hand and just large enough to carry a battery and a small motor. Six leg mechanical spiders can be applicable for the making of robots. It has a wide range of application in the manufacturing of robots. A large version could use existing surveillance technology to convert your television into a real-time look at the world within transmitting range. It would also relay commands from the remote to the spider bike; additional frequencies could be used to operate manipulators for retrieving the mail during unfavorable weather or taking the dog out. In toy industries for making robotic toys it has got many applications. It can also be used for military purpose. By placing bomb detectors in the machines we can easily detect the bomb without harmful to humans. It can be used as heavy tanker machines for carrying bombs as well as carrying other military goods. It is also applicable in the goods industries for the small transportation of goods inside the industry. The mountain roads or other difficulties where ordinary vehicles cannot be moved easily can be replaced by our six leg mechanical spider. Heavy loads can be easily transported if we made this as a giant one. It has got further application for the study of linkage mechanism and kinematic motions. The geometry and conditions can be changed according to application needs. It can travel in rough surfaces very easily, so this machine can be used in rough surfaces were ordinary moving machine cannot travel.

ADVANTAGES

Construction expense is low.
Heavy load can be carried.
It can be run in rough surfaces
Easy to control Maintenance is less

DISADVANTAGES

Speed is minimum due to load.
Not smooth running.
High powered motor is needed

FURTHER POSSIBLE UPGRADATIONS

The spider linkage is a basic concept similar to a wheel made out of stone. Wheels today are still round but improvements in materials,

Construction, drive train, braking, and suspension have increased their usefulness and efficiency. They are used on a wide spectrum of things from small toys to huge pieces of mining equipment. This linkage will evolve in much the same way. Different uses will have different requirements that will drive modifications and advancements. Some of the obvious ones are listed here.

Foot Design

There will be a general-purpose foot designed for a variety of terrain types that could handle sand, rocks, or pavement. Specialized feet will be developed to target specific conditions such as sidewalks, curbs, or stairs and for amphibious vehicles that are expected to travel in wet marshy areas or extreme rock climbing vehicles requiring more traction. Suspension

There are several areas that could be utilized for adding suspension. The foot, leg, shock absorbing links, or attachment points to the frame are several possibilities.Collapsible

The frame and legs for small and mid-sized applications would benefit from a collapsible configuration to increase options for storage and delivery to target. A parallel linkage between the frame and each pair of legs similar to ATV suspensions could be exaggerated to allow the legs to fold up against the body when fully lifted. Amphibious

The legs can function as oars enabling the vehicle to paddle in the water. This could be a passive design such as fixed canards, hinged flaps, or openings designed into the legs that would minimize the drag during the forward stroke on the portions of the leg that are not lifted above the waterline and take advantage of the motion of the leg on the return stroke to propel the vehicle forward. A midpoint on the foldable suspension mentioned above would position the legs to optimize the movement of the legs when rowing. A walking machine with the ability to climb over obstacles and swim across rivers would eliminate many of the restrictions of conventional vehicles. Leading Edge Spurs

Teeth on the front edge of the legs allow the spider to step onto obstacles taller than its step height, the highest point of the foot during a cycle. The downward motion of the leading leg will lift the body of the device if the spurs remain engaged until the paired leg contacts the obstacle and continues to increase the overall center of gravity. Trailing Undercarriage Spurs

A single large protrusion on the trailing edge of each leg, if appropriately designed, would enable the vehicle to crawl over obstacles that would otherwise limit it based on ground clearance. The translation and rotation of the leg during the propelling portion of the cycle can be transferred with this modification. Spring Assist

The use of springs to counter balance the momentum of the legs as they move throughout the cycle would have benefits. The ideal configuration would use springs with the appropriate stiffness to create a system at resonance for a specific target speed. Buckling Leg

Toys would benefit from a leg that would unsnap or provide spring-loaded relief when stepped on or dropped. Larger vehicles could be designed with shear pins or breaking points that would minimize structural damage during collisions, jumps and falls. Hybrid Legs

Additional degrees of freedom could be added to the device by controlling the length of various links with actuators. The added complexity could have benefits. It would allow for precision placement of the foot, increased step height, and still allow high speed traveling when the standard length is locked in. Speed-Leveling Drive Train

The variation in the speed of the foot for a constant rotational speed of the crank is not desirable. A variable crank rotation that could compensate for these differences as well as the mechanical advantage needed when stepping onto obstacles would minimize the stresses on the drive trains of larger vehicles.

CONCLUSION

Skating motion with passive wheels under sustaining ground contact is discussed. The basic idea was to predefine a velocity of the robot and to analyze the resulting motion the skate is forced in. Since the wheels are