Robotics 2 E Part 13 doc

To avoid skewing in the jaws, solutions like those shown in Figure 9.25a orb are used... In case e we see how the addition ofparallelograms 5 as in the example in Figure 9.25b to the mec

FIGURE 9.23f) Idea of a "trunk" made of

Stewart-platform-like elements This ideabelongs to Dr A Sh Kiliskor

9.4 Grippers

In previous sections we have discussed the kinematics and dynamics of lators Now let us consider the tool that manipulators mainly use—the gripper Tomanipulate, one needs to grip and hold the object being manipulated Grippers ofvarious natures exist For instance, ferromagnetic parts can be held by electromag-netic grippers This gripping device has no moving parts (no degrees of freedom and

manipu-no drives) It is easily controlled by switching the current in the coil of the magnet on or off However, its use is limited to the parts' magnetic properties, andmagnetic forces are sometimes not strong enough When relatively large sheets arehandled, vacuum suction cups are used; for instance, for feeding aluminum, brass,steel, etc., sheets into stamps for producing car body parts Glass sheets are also handled

electro-in this way, and some prelectro-intelectro-ing presses use suction cups for grippelectro-ing paper sheets andintroducing them into the press Obviously, the surface of the sheet must be smoothenough to provide reliability of gripping (to seal the suction cup and prevent leakage

of air and loss of vacuum) Here, also, no degrees of freedom are needed for gripping.The vacuum is switched on or off by an automatically controlled valve (We illustratedthe use of such suction cups in the example shown in Figure 2.10.)

Grippers essentially replace the human hand If the gripping abilities of a ical five-finger "hand" are denoted as 100%, then a four-finger hand has 99% of itsability, a three-finger hand about 90%, and a two-finger hand 40%

mechan-We consider here some designs of two-fingered grippers In the gripper shown inFigure 9.24, piston rod 1 moves two symmetrically attached connecting links 2 which

in turn move gripping levers 3, which have jaws 4 (Cylinder 5 can obviously be replaced

by any other drive: electromagnet, cable wound on a drum driven by a motor, etc.)The jaws shown here are suitable for gripping cylindrical bodies having a certain range

of diameters Attempts to handle other shapes or sizes of parts may lead to rical gripping by this device, because the angular displacements of jaws may not beparallel To avoid skewing in the jaws, solutions like those shown in Figure 9.25a) orb) are used In Case a) a simple cylinder 1 with piston 2 and jaws 3 ensures parallel

asymmet-9.4 Grippers 351

FIGURE 9.24 Design of a simple mechanical gripper

FIGURE 9.25 Grippers with translational jaw motion

displacement of the latter In case b) a linkage as in Figure 9.24, but with the addition

of connecting rods 6 and links 7 with attached jaws 4, provides the movement needed.These additional elements create parallelograms which provide the transitional move-ment of the jaws

Various other mechanical designs of grippers are possible For instance, Figure 9.26shows possible solutions a) and b) with angular movement of jaws 1, while cases c)and d) provide parallel displacement of jaws 1 In all cases the gripper is driven by rod

2 All the cases presented in Figure 9.26 possess rectilinear kinematic pairs 3 duction of higher-degree kinematic pairs are shown in Figure 9.27 In case a) cam 1fastened on rod 2 moves levers 3 to which jaws 4 are attached Spring 5 ensures thecontact between the levers and the cam In case b) the situation is reversed: cams 1are fastened onto levers 3 and rod 2 actuates the cams, thus moving jaws 4 Spring 5closes the kinematic chain In case c), which is analogous to case b), springs 5 also playthe role of joints In case d) the higher-degree kinematic pair is a gear set Rack 1 (moved

Intro-by rod 2) is engaged with gear sector 3 with jaws 4 attached to them Cases a) to d)have dealt with angular displacement of jaws In case e) we see how the addition ofparallelograms 5 (as in the example in Figure 9.25b)) to the mechanism shown in Figure9.27d) makes the motion of the jaws translational The last two cases do not needsprings, since the chain is closed kinematically

FIGURE 9.26 Designs of grippers using low-degree kinematic pairs.

FIGURE 9.27 Designs of grippers using high-degreekinematic pairs

9.4 Grippers 353

To describe these mechanisms quantitatively we use the relationships between:

1 Forces F G which the jaws develop, and the force F d which the driving rod applies;and

2 The displacements S d of the driving rod and the jaws of the gripper SG

Figure 9.28 illustrates these parameters and graphically shows the functions SG(Sd) and

F G /Fd=flSj for a gripper.

This discussion of grippers has been influenced by the paper by J Volmer, nische Hochschule Karl-Marx-Stadt, DDR, Mechanism fur Greifer von Handhaberg-eraten," Proceedings of the Fifth World Congress on Theory of Machines andMechanisms, 1979, ASME We should note that the examples of mechanical grippersdiscussed above permit a certain degree of flexibility in the dimensions of parts thegripper can deal with This property allows using these grippers for measuring For

"Tech-instance, by remembering the values of S d by which the driving rod moves to grip theparts, the system can compare the dimensions of the gripped parts

When the manipulated parts are relatively small and must be positioned accurately,miniaturization of the gripper is required A solution of the type shown in Figure 9.29can be recommended, for example, in assembly of electronic circuits Here, the gripper

FIGURE 9.28 Characteristics of amechanical gripper

is a one-piece tool made of elastic material that can bend and surround the gripped

part, of diameter d, to create frictional force to hold the part, and then to release it when it is fastened on the circuit board The overlap h = Q.2d serves this purpose.

Three-fingered grippers are also available (or can be designed for special purposes).Figure 9.30 shows a concept of a three-fingered gripper Part a) presents a general viewand part b) shows a side view Here, 1 is the base of the gripper and 2 the driving rod,which is connected by joints and links to fingers 3 When rod 2 moves right, the fingersopen, and when it moves left, they close This gripper (as well as some consideredearlier) can grip a body from both the outside and the inside (Such grippers are pro-duced by Mecanotron Corporation, South Plainfield, New Jersey, U.S.A.)

One of the most serious problems that appears in manipulators equipped with ferent sorts of grippers is control of the grasping force the gripper develops Obviously,there must be some difference between grasping a metal blank, a wine glass, or an egg,even when all these objects are the same size This difference is expressed in the dif-ferent amounts of force needed to hold the objects and (what is more important) thelimited pressure allowed to be applied to some objects Figure 9.31 shows a possiblesolution for handling tender, delicate objects Here, hand 1 is provided with two elastic

dif-FIGURE 9.30 Three-fingered gripper

FIGURE 9.31 A soft gripper for graspingdelicate objects

9.4 Grippers 355

pillows 2 When inflated by a controlled pressure, they develop enough force to holdthe glass, while keeping the pressure on it small enough to prevent damage (The smallpressure creates considerable holding force due to the relatively large contact areabetween the glass and the pillows.) It is a satisfying solution when modest accuracy ofpositioning is sufficient

A more sophisticated approach to the problem of handling delicate objects is the

Utah-MIT dextrous hand which is described in the Journal of Machine Design of June

26, 1986 This is a four-fingered hand consisting of three fingers with four degrees offreedom and one "thumb" with four degrees of freedom The "wrist" has three degrees

of freedom The thumb acts against the three fingers Thus, the hand consists of 16movable links driven by a system of pneumatically operated "tendons" and 184 low-friction pulleys The joints connecting the links include precision bearings The problem

of air compressibility is overcome by use of special control valves Figure 9.32a) shows

a general design of one finger Here links A, B, and C can rotate around their joints.The space inside the links is hollow and contains the pulleys and the tendons, which

go around the pulleys and are fastened to the appropriate links Figure 9.32b) showsthe drive of link C Tendons I and la run around pulleys 7, 8, and 9 and are fastened tothe center of pulley 6 Thus, pulling tendons I and la causes bending and straighten-ing of link C Figure 9.32c) shows the control of link B by tendons II and Ha, and Figure9.32d) shows the control of link A by tendons III and Ilia A pair of tendons IV and IVaare used for turning the whole finger around the X-Xaxis, as shown in Figure 9.32e).The Utah-MIT hand has 16 position sensors and 32 tendon-tension sensors Thus itsgrasping force can be controlled, and the object handled by the gripper with a light orheavy touch

For simpler grippers (as in Figures 9.24, 9.28, and 9.30), force-sensitive jaws can bemade as shown in Figure 9.33 Here, part 1 is grasped by jaws 2 which develop grasp-

ing force F G The force is measured by sensor 3 located in base 4 which connects the

gripper with drive rod 5 The latter moves rack 6 and the kinematics of the gripper

Force F d , which is developed by rod 5, determines grasping force FG Sensor 3 enables

the desired ratio F G /F d to be achieved The sensor can be made so as to measure morethan one force, say, three projections offerees and torques relative to a coordinate axis.These devices help to control the grasping force; however, its value must be pre-determined (before using the gripper) and the system tuned appropriately Seriousefforts are being devoted to simulating the behavior of a human hand, which "knows"how to learn the required grasping force during the grasping process itself This ability

of a live hand is due to its tactile sensitivity Next, we consider some concepts of ficial tactile sensors installed inside the gripper's fingers or jaws Figure 9.34 illustrates

arti-a design for arti-a one-dimensionarti-al tarti-actile sensor larti-aws 1 develop grarti-asping force F G which

must cause enough frictional force F u (vertically directed) to prevent object 2 from

falling due to gravitational force P The sensor consists of roller 3 mounted on shaft 4

by means of bearings Shaft 4 is mounted on jaw 1 by flat spring 5, which presses roller

3 against object 2 through a window in the jaw When F u < P, slippage occurs between the gripper and object, and the object moves downward for a distance X, thus rotat-

ing roller 3 (see the arrow x in the figure) This rotation is translated into electric signals(say, pulses, due to an encoder located between shaft 4 and the inner surface of hollow

roller 3), which cause the control system to issue a command to increase force F G untilthe slippage stops (but no more than that, to prevent any damage to the object) In

FIGURE 9.32 Design of the Utah-MIT dextrous hand: a) General view of

one finger; b) Drive of link C; c) Drive of link B; d) drive of link A; e) Turning

around the X-X axis

addition, the control system also gives a command to lift the gripper for a distance Y

to compensate for the displacement X due to the slippage.

For two-dimensional compensation, the concept shown in Figure 9.35 can be posed Here conducting sphere 1 (instead of a roller) is used The surface of this sphere

pro-is covered with an insulating coating in a checkered design Three (at least) contacts

2,3, and 4 touch the sphere and create a circuit in which a constant voltage V

ener-gizes the system When slippage occurs between object 5 and the gripper, the sphere

9.4 Grippers 357

FIGURE 9.33 Design of a grasp-force-sensitive gripper

FIGURE 9.34 One-dimensionaltactile sensor

rotates and voltage pulses V 1 and V 2 correspond to the direction of the slippage vector

S relative to the X- and Y-coordinates A layer of soft material 6 is used to protect thesphere from mechanical damage

The jaws or fingers discussed in this section can be provided with special insertsand straps to better fit the specific items the grippers must deal with For handling toolslike drills, cutters, probes, etc., the straps must go round their shaft and provide

FIGURE 9.35 Two-dimensional tactile sensor.accuracy and reliability of grasping The same idea is used for making the jaws corre-spond to other specific shapes, dimensions, and materials of items being processed.Special devices can be considered for holding exchangeable grippers, say, to replace atwo-finger gripper with a three-finger one during the processing cycle, which may beeffective in some cases.

9.5 Guides

The problem of designing guides is mainly specific for X-Y tables which,

accord-ing to our classification, belong to Cartesian manipulators with two degrees of freedom.However, the concept of guides can be generalized and applied more broadly (exceptfor translational movement) also to polar or rotating elements as well as to spiral guides(screws) Guides must provide:

• Stable, accurate, relative disposition of elements;

• Accurate performance of relative displacements, whether translational or angular;

• Low frictional losses during motion;

• Wear resistance for a reasonable working lifetime;

• Low sensitivity to thermal expansion (and compression) to maintain the requiredlevel of accuracy

These properties must be achieved within the limits of reasonable expense and nical practicality The designer faces contradictory conditions in trying to meet theserequirements In certain cases the weight of the structure must be minimized, e.g., formoving links such as manipulator links For accuracy, the guides must be rigid to preventdeflections For heavier loads, the area of contact between the guide and the moving

tech-9.5 Guides 359part must be larger To prevent excess wear, the guides must apply low pressure to themoving part, which also entails a certain width of the guide and length of the support(to create the required contact area) It is important to mention that, above all, wear ofthe guides depends on the maintenance and operating conditions Wear varies from 0.02

mm per year for good conditions to 0.2 mm per year for careless operation We discusshere some ideas and concepts for overcoming some of these technical obstacles.Figure 9.36 shows a typical example of a Cartesian guide system for a lathe and the

scheme of forces acting in the mechanism Guides 1 along axis X-X (main guides of the bed shown in projection b)) and guides 2 along axis Y-Yin dovetail form (its cross

section is shown in projection a)) direct the support 4 of cutter 3 The cutter develops

force P at the cutting point Decomposition of this force yields its three components

P x , Py, and P z Together with the weight G of the moving part, these forces cause the

guides to react with forces A, B, and Cin the Z-Fplane and frictional forces f A , f B , and

f c along the X-axis (when movement occurs) Statics equations permit finding the

reac-tive forces A, B, C, and Q:

FIGURE 9.36 Two-dimensional Cartesian guide system and forces acting in it

Here, X, Y, and Z are components of acting forces, and T x> T Y , T z are components ofacting torques (Two other equations and one additional condition permit figuring out

the coordinates X A , X B , and X c where the forces are applied, but we do not consider

this calculation here.) When A, B, and C are defined, the corresponding pressures can

be calculated:

Here a, b, c, and L are geometrical dimensions of the guides and are shown in Figure 9.36.

The obtained pressure values are average values, and the real local pressure mightnot be uniformly distributed along the guides The allowed maximum pressures depend

on the materials the guides are made of and their surfaces, and are about 300 N/cm2for slow-moving systems to 5 N/cm2 for fast-running sliders Obviously, the lower thepressure, the less the wear and the thicker the lubricant layer and, as a result, smaller

frictional forces f A ,f B , and/c appear in the mechanism

Figure 9.37 shows some common shapes of heavy-duty translational guides Theprismatic guides in cases a) and b) are symmetrically shaped and those in cases c) andd) are asymmetrical Cases b) and d) are better for holding lubricant; however, theseshapes collect dirt of various kinds, which causes increased wear In contrast, cases a)and c) have less ability to hold lubricant, but do not suffer from trapped dirt Cases a)and f) are dovetail-type guides This type of guide can be used not only for guiding hor-izontal movement (like cases a), b), c), and d)) but also for vertical or even upside-downorientation of the slider The difference between cases e) and f) is the pairs of matingsurfaces: lower and side surfaces in case e) and upper and side surfaces in case f) Casee) is more expensive to produce but easier to lubricate, while case f) is easier to producebut worse at holding lubricant Rectangular guides—cases g) and h)—are cheaper andsimpler to produce and also provide better precision However, this shape is worse forlubrication and is sensitive to dirt, especially when the dirt is metal chips which scratchthe surface, causing wear and increasing friction The cylindrical guides in cases i) andj) have the same properties as the prismatic guides but are simpler to produce

To provide the required level of precision and smoothness of action, special devicesare used to decrease play Figure 9.38 illustrates some common means of backlashadjustment Cases a), b), and c) show rectangular guides In case a) vertical and hori-

FIGURE 9.37 Cross sections of translational guides

9.5 Guides 361

FIGURE 9.38 How to decrease play and adjust backlash in translational guides to therequired values: a), b), c) Flat rectangular guides; d), e), f), g), h), i) Dovetail guides;

m), n), o) Cylindrical guides; k), 1) Wedges for adjustment

zontal backlash is eliminated by wedges la, Ib, and 2, respectively Purely horizontalmovement, case b), can be controlled with only one wedge 4, while vertical play istaken up by straps 1 and 2 Sometimes spacers 1 (case c)) are used for more preciselimitation of backlash The wedges are usually mounted with special bolts or screws(3 in Figure 9.38b or as shown in Figures 9.38k) and 1)) Screwing (or unscrewing) bolts

1 moves wedge 2 in the desired direction relative to housing 3, closing or opening thegap In Figures 9.38d), e), f), g), and h) are shown various ways to adjust the wedgesvia bolts 1 and spacers 2 For dovetail guides (case i)), only one wedge 1 is needed tosolve the play problem To control play in cylindrical guides (case m)), strap 1 withspacers 2 can be used, or an elastic design with a bolt closing gap A (as in case n)), or

a split conical bushing 1 (case o))

A serious problem arises when these frictional guides are used, which is associatedwith frictional forces and leads to not only driving power losses but also (and oftenthis is more important) limited accuracy It is worthwhile to analyze this problem in

greater depth Frictional force F F appearing in a slide pair depends on the speed of

rel-ative motion x, as shown in Figure 9.39 This means that, when the speed is close to 0, the frictional force F ST is higher than it is at faster speeds Thus,

Here F is the driving force, and Fdin is the frictional force at the final sliding speed

This can be analyzed further with the help of Figure 9.40 Mass M of the slider is driven by force F through a rod with a certain stiffness c (This can be and often is a

lead screw, piston rod, rack, etc.) From the layout in Figure 9.40 it follows that the mass

essentially does not move until F reaches F ST This entails deformation X ST of the rod,which can be calculated as

At the moment when movement begins (x> 0), mass Mis under the influence of a

composite moving force:

FIGURE 9.39 Frictional force versus speed

FIGURE 9.40 Calculation model for friction

as in Figure 9.39

9.5 Guides 363

It thus follows that, even if at that moment F is changed to 0, some displacement

of the mass will take place An equation approximately describing this movement andtaking Expression (9.51) into account is

Force Fdin is a function of x Let us suppose that it is justified to express this

func-tion in the following way (see Figure 9.39):

Then we can rewrite and simplify Equation (9.52) as follows:

(Here Expression 9.50 is substituted; therefore 0 appears on the right side.) The tion has the form

solu-By substituting this solution into Equation (9.53), we obtain the following

expres-sions for a and CD:

Under the initial conditions (when t = 0) the displacement x = X ST , and speed x = 0.

So we obtain for the coefficients A and B

Thus, finally, the solution is

For instance, for M- 100 kg, c = 104 N/cm, F ST = 100 N and a = 1 Nsec/m, we find

from (9.50) that

and from (9.55) that

The ratio z = x/x ST is shown in Figure 9.41 as a function of time An analytical

approx-imation expressing the dependence between the friction force F and the sliding speed

FIGURE 9.41 Motion-versus-time diagram from the calculation

model shown in Figure 9.40

V may be convenient in engineering applications This approximation may have the

following form:

For x(f) as displacement we have V= x(t).

When using computer means, for example, MATHEMATICA, we can simplify thiscomputation by introducing this approximation for describing the friction versus speedbehavior of the slider as follows:

q2=Plot[200 (((1 + EAVA(-l))A(-i) 5) 05 v),{v,-5,5}]

Figure 9.4 la shows the form of the "friction force versus speed" dependence which

is close to the experimentally gained results

FIGURE 9.41 a) Friction force versus speed dependence using the

above-given approximation; here a = 0.5 and b = 0.05