MECHANICAL SPIDER- GQ64

1. INTRODUCTIONGQ64 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 Muter drive Chain and sprocket drive 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 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 which 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 axialconnecting 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.

1.1WHAT IS GQ64? G - General Q - Quadric System6 - Six Links 4 - Four Legs

Fig. 1 Mechanical Spider 1.2 MECHANISMS USED 1.2.1 Klenn mechanistic mechanismKlenn 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 consists 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 Klenn 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.

Fig. 2 Klenn mechanistic mechanism chain

1.2.2 Anatomy of SpiderMost insects have three body parts. Spiders and other arachnids have only two major body parts. The anterior part is called the cephalothoraxesOr prosoma and the posterior part are called abdomen, or opisthosoma.Spiders have eight legs attached to the cephalothoraxes 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 (macro setae) 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 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.

Spider LegsIn 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.

1.3 TRANSMITTING SYSTEMWhich 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 .

1.3.1 Main type of transmitting 1. Mechanical spider with gear mechanism2. Mechanical spider without gear

1.3.2 MotivationTo 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 does 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.

1. BASIC STUDY ABOUT MECHANISM2.1 Planar and Spatial MechanismsMechanisms can be divided into planar mechanisms and spatial mechanisms, 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 mechanismsare 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.A little consideration will show that a mechanism may be regarded as a machine in which each part is reduced to the simplest form to transmit the required motion.1.1.1 NUMBER OF DEGREES OF FREEDOM FOR PLANAR MECHANISMIn 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.

Fig. 3 Mechanisms Schismatic Diagram of Mechanical Spider

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 numberOf movable links will be (l 1) and thus the total number of degrees ofFreedom will be 3 (l 1) before they are connected to any other link. InGeneral, 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 theNumber of degrees of freedom of a mechanism is given by- n = 3 (l 1) 2 j hKutzbach Criterion to Plane Mechanisms n = 3 (l 1) 2 j hGrublers Criterion for Plane MechanismsThe Grublers 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 = 0This 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 = 3.2Kinematics and Dynamics of Mechanisms.

2.2 KINEMATICS, KINETICS, DYNAMICS

Kinematicsof 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.Kineticsdeals with action of forces on bodies. This is where the effects of gravity come into play.Dynamicsis the combination ofkinematicsandkinetics. Dynamicsof 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.

2.3 LINKS, FRAMES AND KINEMATICS CHAIN

Alinkis defined as a rigid body having two or more pairing elements which connect it to other bodies for the purpose of transmitting force or motion in every machine, at least one link either occupies a fixed position relative to the earth or carries the machine as a whole along with it during motion. This link is theframeof the machine and is called thefixed link.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 needs 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, and2. It must be a resistant body

2.3.1 Types of LinksPiston and piston rod of an IC engine. 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.

2.4 KINEMATIC PAIRThe 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. First of all, let us discuss the various types of constrained motions.

2.4.1 Types of Constrained MotionsFollowing are the three types of constrained motions: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. 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.

2. Incompletely constrained motionWhen 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, as shown in Fig. 5.4, 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.

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. Consider a shaft I .The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely con-strained 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.

2.4.2 Classification of Kinematic PairsThe kinematic pairs may be classified according to the following considerations:1. 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:(a) 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.(b) 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.(c) 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.(d) 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.(e) 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.

2. 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:(a) 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.(b) 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. Pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings and cam and follower is the examples of higher pairs.3. According to the type of closure. The kinematic pairs according to the type of closure between the Elements may be classified as discussed below:(a) 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.(b) 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.

3. INVERSION OF MECHANISMSWe 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 byFixing different links in a kinematic chain is known as inversion of the mechanism.

1. Four bar chain or quadric cyclic chain, 2. Single slider crank chain, and3. Double slider crank chain.

3.1 Concept DeterminationSeveral 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

Fig. 4 Motion of Leg

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.

Fig. 5 Final Motion

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.3.2 SKATINGIn 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

3.2.1 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.

4. KLENN MECHANISTIC MECHANISMThis 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.

Fig. 6 Graphical Motion of Legs

4.1 MOTION- (pictorial representation)FIG. 7 Diagram of MotionFig. 7 (a)

Fig. 7 (b)

Fig. 7 (c)

Fig. 7 (d)

Fig. 7 (e)

Fig. 7 (f)

Fig. 7 (g)

Fig. 7 (h)

The Klenn 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 does not require microprocessor control or multitudes of inefficient actuator mechanisms. It fits into the technological void between these walking devices and axel-driven wheels.

5. FINIAL MECHANISM

Fig. 8

Fig. 95.1 SYSTEM OVERVIEW

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

5.2 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 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 angle ranges from the minimum of 94 to the maximum of 46 degrees.

5.3 RESTRICTIVE FACTORSUntil 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.

5.4 THE EQUILIBRIUM LINEThe 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 current angle has the same value as the 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.

6 MECHANICAL DESIGN OF SKATES6.1 RequirementsFor 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 position6.2 Results of the Sector ApproachFor 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.

7. APPLICATIONSPotential 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 spiderlike. 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.

8. FURTHER POSSIBLE UPGRADATIONSThe spiderlike 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.

FootDesign

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 severalpossibilities.

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 ofconventionalvehicles.

LeadingEdge 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.

TrailingUndercarriageSpurs

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 thismodification.

SpringAssist 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 resonanceforaspecifictargetspeed.BucklingLeg

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.

HybridLegs

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-LevelingDriveTrain

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.

9. CONCLUSIONSkating 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 areModeled as perfect skates, the possible movement is strongly restricted by the constraint for perfect skates, which forbids movement in axial direction.

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