Sandin P.E. Robot mechanisms and mechanical devices illustrated

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234 Chapter 9 Comparing Locomotion Methods

really, that can climb slopes that a wheeled or tracked vehicle simply

could not get up. Negotiable slope angle is therefore important, but it

should be assumed that the material in ground contact is the same no

matter what type of mobility system is used.

Obstacles

Obstacles can also be scaled, but they create a special case. The effec-

tiveness of the mobility system could be judged almost entirely by how

high, relative to its elevation area, an obstacle it can negotiate. Obstacle

negotiation is a little more complicated than that but it can be simplified

by dividing it into three subcategories.

• Mobility system overall height to negotiable obstacle height

• System length to negotiable obstacle height

• System elevation area to negotiable obstacle height

The comparison obstacle parameters can be defined to be the height of

a square step the system can climb onto and the height of a square topped

wall the system can climb over without high centering, or otherwise

becoming stuck.

An inverted obstacle, a chasm, is also significant. Negotiable chasm

width is mostly a function of the mobility system’s length, but some

clever designs can vary their length somewhat, or shift their center of

gravity, to facilitate crossing wider chasms. For systems that can vary

their length, negotiable chasm width should be compared using the sys-

tem’s shortest overall length. For those that are fixed, use the overall

length.

Another facet of obstacle negotiation is turning width. This is impor-

tant because a mobility system with a small turning radius is more likely

to be able to get out of or around confining situations. Turning width is

not directly a function of vehicle width, but is defined as the narrowest

alley in which the vehicle can turn around. This is in contrast to ratings

given by some manufacturers that give turning radius as the radius of a

circle defined as the distance from the turning point to the center of the

vehicle width. This can be misleading because a very large vehicle that

turns about its center can be said to have a zero-radius turning width.

A turning ability parameter must also show how tightly a vehicle can

turn around a post, giving some idea how well it could maneuver in a for-

est of closely spaced trees. There are, then, two width parameters, alley

width and turning-around-a-post width.

Chapter 9 Comparing Locomotion Methods 235

COMPLEXITY

A more nebulous comparison criteria that must be included in an evalua-

tion of any practical mechanical device is its inherent complexity. A

common method for judging complexity is to count the number of mov-

ing parts or joints. Ball or roller bearings are usually counted as one part

of a joint although there may be 10s of balls or rollers moving inside the

bearing. A problem with this method is that some parts, though moving,

have very small forces on them or operate in a relatively hazard-free

environment and, so, last a very long time, sometimes even longer than

nonmoving parts in the same system.

A second method is to count the number of actuators since their num-

ber relates to the number of moving parts and they are the usually the

source of greatest wear. The drawback of this method is that it ignores

passive moving parts like linkages that may well cause problems or wear

out before an actively driven part does. The first method is probably a

better choice because robots are likely to be moving around in com-

pletely unpredictable environments and any moving part is equally sus-

ceptible to damage by things in the environment.

Speed and Cost

There are two other comparison parameters that could be included in a

comparison of mobility methods. They are velocity of the moving vehi-

cle and cost of the locomotion system. Moving fast over rough and

unpredictable terrain places large and complex loads on a suspension

system. These loads are difficult to calculate precisely because the ter-

rain can be so unpredictable. Powerful computer simulation programs

can predict a suspension system’s performance with a moderate degree

of accuracy, but the suspension system still must always be tested in the

real world. Usually the simulation program’s predictions are proven

inaccurate to a significant degree. It is too difficult to accurately predict

and design for a specific level of performance at speeds not very far

above eight m/s to have any useful meaning. It is assumed that slowing is

an acceptable way to increase mobility, and that slowing can be done

with any suspension design. Mobility is not defined as getting over an

obstacle at a certain speed; it is simply getting over the obstacle at what-

ever speed works.

Cost can be related to size, weight, and complexity. Fewer, smaller,

and lighter parts are usually cheaper. The design time to get to the sim-

plest, lightest design that meets the criteria may be longer, but the end

cost will usually be less. Since cost is closely related to size, weight, and

236 Chapter 9 Comparing Locomotion Methods

complexity, it does not need to be included in a comparison of suspen-

sion and drive train methods.

THE MOBILITY INDEX COMPARISON METHOD

Another, perhaps simpler, method is to create an index of the mobility

design’s capabilities listed as a set of ratios relating the mobility system’s

length, height, width, and possibly complexity, to a small set of terrain

parameters. The most useful set would seem to be obstacle height, cre-

vasse width, and narrowest alley in which the vehicle can turn around.

Calculating the vehicle’s ground pressure would cover mobility in sand

or mud. The pertinent ratios would be:

• Step/Elevation Area: Negotiable step height divided by the elevation

area of mobility system

• Step/System Height: Highest negotiable wall or platform, whichever

is shorter, divided by mobility system height

• Crevasse/System Length: Negotiable crevasse width divided by vehi-

cle length (in the case of variable geometry vehicles, the shortest

length of the mobility system)

• System Width/Turning diameter: Vehicle width divided by outermost

swept diameter of turning circle

• System Width/Turning-Around-a-Post Width: Vehicle width divided

by width of path it sweeps when turning around a very thin post

• Ground Pressure

These are all set up so that a higher ratio number means theoretically

higher mobility. No doubt, some mobility system designs will have very

high indexes in some categories, and low indexes in others. Having a sin-

gle Mobility Index for each mobility system design would be convenient,

but it would be difficult to produce one that describes the system’s abili-

ties with enough detail to be useful. These six, however, should give a

fairly complete at-a-glance idea of how well a certain design will per-

form in many situations.

THE PRACTICAL METHOD

A third way to compare mobility systems that may work well for a

designer working on a specific robot design, is to calculate the total vol-

Chapter 9 Comparing Locomotion Methods 237

ume of everything on the robot not related to the mobility system

(including the power supply), and define this volume with a realistic

ratio of length, width, and height. A good place to start for the size ratios

is to make the width 62 percent of the length, and the height one quarter

of the length. This box represents the volume of everything the mobility

system must carry.

The next step is to define the mobility requirements, allowing sub-

stantial leeway if the operating environment is not well known. The basic

six parameters discussed above are a good place to start.

• Step or wall height

• Minimum tunnel height

• Crevasse width

• Maximum terrain slope

• Minimum spacing of immovable objects

• Maximum soil density

All of these need to be studied carefully to aid in determining the most

effective mobility system layout to use. The more time spent doing this

study, the better the mobility system choice will match the terrain’s

requirements.

When this study is completed, selecting and designing the mobility

system is then a combination of scaling the system to the robot’s box

size, and meeting the mobility constraints. It should be remembered that

this process will include several iterations, trial and error, and persever-

ance to guarantee that the best system is being incorporated. The more

information that can be obtained about the operating environment, the

more likely the robot will be successful. In the end, one of the more

capable and versatile mobility systems, like the six-wheeled rocker bogie

or the four-tracked front-flipper layouts will probably work well enough

even without complete knowledge of the environment.

A generic rule of thumb for mobility system design can be extracted

from the investigations done in this chapter. Relative to the size and

weight of the vehicle the mobility system is carrying, make the mobility

system big, light, slow, low (or movable) cg, and be sure it has sufficient

treads. If all these are maximized, they will make your robot a high

mobility robot.

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Chapter 10 Manipulator Geometries

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anipulator is a fancy name for a mechanical arm. A manipulator is

an assembly of segments and joints that can be conveniently

divided into three sections: the arm, consisting of one or more segments

and joints; the wrist, usually consisting of one to three segments and

joints; and a gripper or other means of attaching or grasping. Some texts

on the subject divide manipulators into only two sections, arm and grip-

per, but for clarity the wrist is separated out as its own section because it

performs a unique function.

Industrial robots are stationary manipulators whose base is perma-

nently attached to the floor, a table, or a stand. In most cases, however,

industrial manipulators are too big, use a geometry that is not effective

on a mobile robot, or lack enough sensors -(indeed many have no envi-

ronmental sensors at all) to be considered for use on a mobile robot.

There is a section covering them as a group because they demonstrate a

wide variety of sometimes complex manipulator geometries. The chap-

ter’s main focus, however, will be on the three general layouts of the arm

section of a generic manipulator, and wrist and gripper designs. A few

unusual manipulator designs are also included.

It should be pointed out that there are few truly autonomous manipu-

lators in use except in research labs. The task of positioning, orienting,

and doing something useful based solely on input from frequently inade-

quate sensors is extremely difficult. In most cases, the manipulator is

teleoperated. Nevertheless, it is theoretically possible to make a truly

autonomous manipulator and their numbers are expected to increase dra-

matically over the next several years.

POSITIONING, ORIENTING, HOW MANY

DEGREES OF FREEDOM?

In a general sense, the arm and wrist of a basic manipulator perform two

separate functions, positioning and orienting. There are layouts where

the wrist or arm are not distinguishable, but for simplicity, they are

treated as separate entities in this discussion. In the human arm, the

241

242 Chapter 10 Manipulator Geometries

shoulder and elbow do the gross positioning and the wrist does the ori-

enting. Each joint allows one degree of freedom of motion. The theoreti-

cal minimum number of degrees of freedom to reach to any location in

the work envelope and orient the gripper in any orientation is six; three

for location, and three for orientation. In other words, there must be at

least three bending or extending motions to get position, and three twist-

ing or rotating motions to get orientation.

Actually, the six or more joints of the manipulator can be in any order,

and the arm and wrist segments can be any length, but there are only a

few combinations of joint order and segment length that work effec-

tively. They almost always end up being divided into arm and wrist. The

three twisting motions that give orientation are commonly labeled pitch,

roll, and yaw, for tilting up/down, twisting, and bending left/right respec-

tively. Unfortunately, there is no easy labeling system for the arm itself

since there are many ways to achieve gross positioning using extended

segments and pivoted or twisted joints. A generally excepted generic

description method follows.

A good example of a manipulator is the human arm, consisting of a

shoulder, upper arm, elbow, and wrist. The shoulder allows the upper

arm to move up and down which is considered one DOF. It allows for-

ward and backward motion, which is the second DOF, but it also allows

rotation, which is the third DOF. The elbow joint gives the forth DOF.

The wrist pitches up and down, yaws left and right, and rolls, giving

three DOFs in one joint. The wrist joint is actually not a very well

designed joint. Theoretically the best wrist joint geometry is a ball joint,

but even in the biological world, there is only one example of a true full

motion ball joint (one that allows motion in two planes, and twists 360°)

because they are so difficult to power and control. The human hip joint is

a limited motion ball joint.

On a mobile robot, the chassis can often substitute for one or two of

the degrees of freedom, usually fore/aft and sometimes to yaw the arm

left/right, reducing the complexity of the manipulator significantly.

Some special purpose manipulators do not need the ability to orient the

gripper in all three axes, further reducing the DOF. At the other extreme,

there are arms in the conceptual stage that have more than fifteen DOF.

To be thorough, this chapter will include the geometries of all the

basic three DOF manipulator arms, in addition to the simpler two DOF

arms specifically for use on robots. Wrists are shown separately. It is left

to you to pick and match an effective combination of wrist and arm

geometries to solve your specific manipulation problem. First, let’s look

at an unusual manipulator and a simple mechanism—perhaps the sim-

plest mechanism for creating linear motion from rotary motion.

Chapter 10 Manipulator Geometries 243

E-Chain

An unusual chain-like device can be used as a manipulator. It is based on

a flexible cable bundle carrier called E-Chain and has unique properties.

The chain can be bent in only one plane, and to only one side. This

allows it to cantilever out flat creating a long arm, but stored rolled up

like a tape measure. It can be used as a one-DOF extension arm to reach

into small confined spaces like pipes and tubes. Figure 10-1 shows a

simplified line drawing of E-chain’s allowable motion.

Slider Crank

The slider-crank (Figure 10-2) is usually used to get rotary motion from

linear motion, as in an internal combustion engine, but it is also an effi-

cient way to get linear motion from the rotary motion of a motor/gear-

box. A connecting rod length to / crank radius ratio of four to one pro-

duces nearly linear motion of the slider over most of its stroke and is,

therefore, the most useful ratio. Several other methods exist for creating

Figure 10-1 E-chain