12 Sensors and Actuators Jeanne Sullivan Falcon National Instruments 12.1 Encoders Rotary and Linear Incremental Encoders • Tachometer • Quadrature Encoders • Absolute Encoders 12.2 Anal
Trang 1Using ˆa and c, we can define a local coordinate system on the tool defined by the set of mutually orthogonal unit vectors ˆe1, ˆe2, and ˆe3 The local coordinate system is defined as
ˆe1 = ˆa
if|˙ˆa| = 0 then ˆe2= ˙ˆa
if|˙ˆa| = 0 and ˙ˆa · ˙c = 0 then ˆe3= ˆa × ˙c
| ˙c| and ˆe2 = ˆe3× ˆe1
Consider, as depicted in Figure 10.15, the circle defined by the intersection of a plane normal to the
cutting tool’s axis of rotation ˆa, offset from the origin of the tool coordinate system c, by the perpendicular
distance u A point p lies in that plane at an angle θ measured from the axis ˆe2 The velocity of point is
v= ˙c + u|˙ˆa|ˆe2− r (u)|˙ˆa|ˆe1cosθ (10.30)
The unit normal vector to the surface of revolution at point p is
ˆn= −r (u)ˆe1+ ˆe2cosθ + ˆe3sinθ
√
where
r (u)= dr
d z
z =u
(10.32)
n^
a^
e^1
e^3
e^2
Θ
Workpiece Local Coordinate System Cutting Tool
Local Coordinate System Origin
a^
c
c
p
v
FIGURE 10.15 Notation for calculating points on the critical curve.
Trang 2Error Budgeting 10-19
Combining Equation (10.30) and Equation (10.31) into Equation (10.24) yields an equation of the form
where
Equation (10.33) admits a closed form solution
D=
cosθ = C2− AC − B2+ BD
sinθ = ( A − C)(B − D)
The results of Equation (10.38) and Equation (10.39) can be used to compute the positions of the points
p(t, u) on the surface of the working envelope
p(t, u) = c + uˆe1+ r (u)(ˆe2cosθ ± ˆe3sinθ) (10.40) The “±” symbol indicates that there are two solutions for p(t, u) If the tool is cutting a trough, then
both solutions are valid If the tool is contouring counterclockwise as viewed in the positive ˆe3direction, then retain only the solution corresponding to the plus sign If the tool is contouring clockwise as viewed
in the positive ˆe3direction, then retain only the solution corresponding to the minus sign
As is evident from Equation (10.39) above, if A is equal to −C then sin θ is zero, cosθ is one, and θ equals zero For any values of u such that A − C < 0, that cross section of the tool is not in contact with the workpiece surface Similarly, if the value of D is imaginary, the results of the calculation can be safely
disregarded because the cutting tool is again not in contact with the workpiece This occurs only when the tool is plunging at a steep angle so that every point cut by that section of the tool is immediately swept away by the cross sections following behind it
The closed form solution described above can be used in error budgeting by performing three operations:
(1) compute the swept envelope of the cutting tool using a kinematic model with no error motions to determine the nominal machined surface; (2) compute the swept envelope of the cutting tool including
error motions to determine the perturbed machined surface; (3) evaluate the accuracy of the machining
process by comparing the perturbed and nominal machined surfaces The procedure described above has proved useful for modeling form grinding, centerless grinding, and “chasing the pin” cylindrical grinding
It should also be useful for ball end milling and flank milling with conical milling cutters Due to the assumption that the cutter is a perfect surface or revolution, it is most useful for evaluating tolerances of form, profile, location, and size and is probably less useful for surface finish
10.8 Summary
An error budget is a tool for predicting and managing variability in an engineering system This chapter has reviewed basic theory of probability, tolerances, and kinematics and described a framework for error budgeting based upon those theoretical foundations The framework presented here is particularly suited
to manufacturing systems including robots, machine tools, and coordinate measuring machines
Trang 3An error budget must be developed with great care because small mistakes in the underlying assumptions
or the mathematical implementation can lead to erroneous results For this reason, error budgets should
be kept as simple as possible, consistent with the needs of the task at hand When error budgets are scoped appropriately, developed rigorously, and consistent with theoretical foundations (e.g., engineering science, mathematics, and probability), they are an indispensable tool for system design
References
[1] Donaldson, R.R (1980) Error Budgets Technology of Machine Tools, Vol 5, Machine Tool Task
Force, Robert J Hocken, Chairman, Lawrence Livermore National Laboratory
[2] Slocum, A.H (1992) Precision Machine Design Prentice Hall, Englewood Cliffs, NJ.
[3] Soons, J.A., Theuws, F.C., and Schellekens, P.H (1992) Modeling the errors of multi-axis machines:
a general methodology Precision Eng., vol 14, no 1, pp 5–19.
[4] Chao, L.M and Yang, J.C.S (1987) Implementation of a scheme to improve the positioning accuracy
of an articulate robot by using laser distance-measuring interferometry, Precision Eng., vol 9, no 4,
pp 210–217
[5] Frey, D.D., Otto, K.N., and Pflager, W (1997) Swept envelopes of cutting tools in integrated machine
and workpiece error budgeting Ann CIRP, vol 46, no 1, pp 475–480.
[6] Frey, D.D., Otto, K.N., and Taketani, S (2001) Manufacturing system block diagrams and optimal
adjustment procedures ASME J Manuf Sci Eng., vol 123, no 1, pp 119–127.
[7] Frey, D.D and Hykes, T (1997) A Method for Virtual Machining U.S Patent #5,691,909.
[8] Treib, T (1987) Error budgeting — applied to the calculation and optimization of the volumetric
error field of multiaxis systems Ann CIRP, vol 36, no 1, pp 365–368.
[9] Portman, T (1980) Error summation in the analytical calculation of lathe accuracy Machines and Tooling, vol 51, no 1, pp 7–10.
[10] Narawa, L., Kowalski, M., and Sladek, J (1989) The influence of kinematic errors on the profile
shapes by means of CMM Ann CIRP, vol 38, no 1, pp 511–516.
[11] Whitney, D.E., Gilbert, O.L., and Jastrzebski, M (1994) Representation of geometric variations
using matrix transforms for statistical tolerance analysis in assemblies Res Eng Design, vol 6,
pp 191–210
[12] Donmez, A (1995) A General Methodology for Machine Tool Accuracy Enhancement: Theory, Appli-cation, and Implementation, Ph.D thesis, Purdue University.
[13] Ceglarek, D and Shi, J (1996) Fixture failure diagnosis for the autobody assembly using pattern
recognition ASME J Eng Ind., vol 118, no 1, pp 55–66.
[14] Kurfess, T.R., Banks, D.L., and Wolfson, J.J (1996) A multivariate statistical approach to metrology
ASME J Manuf Sci Eng., vol 118, no 1, pp 652–657.
[15] Drake, A.W (1967) Fundamentals of Applied Probability Theory McGraw-Hill, New York [16] ASME (1983) ANSI Y14.5M — Dimensioning and Tolerancing American Society of Mechanical
Engineering, New York
[17] Kane, V.E (1986) Process capability indices J Qual Technol., vol 18, no 1, pp 41–52.
[18] Harry, M.J and Lawson, J.R (1992) Six Sigma Producibility Analysis and Process Characterization.
Addison-Wesley, Reading, MA
[19] Phadke, M.S (1989) Quality Engineering Using Robust Design Prentice Hall, Englewood Cliffs, NJ.
[20] Denavit, J and Hartenberg, R (1955) A kinematic notation for lower pair mechanisms based on
matrices J Appl Mech, vol 1, pp 215–221.
[21] Bryan, J.B (1989) The Abb´e principle revisited — an updated interpretation Precision Eng., vol 1,
no 3, pp 129–132
[22] Lin, P.D and Ehmann, K.F (1993) Direct volumetric error evaluation for multi-axis machines Int.
J Machine Tools Manuf., vol 33, no 5, pp 675–693.
[23] CIRP (1978) A proposal for defining and specifying the dimensional uncertainty of multiaxis
measuring machines Ann CIRP, vol 27, no 2, pp 623–630.
Trang 4Error Budgeting 10-21
[24] Shen, Y.L and Duffie, N.A (1993) Comparison of combinatorial rules for machine error budgets
Ann CIRP, vol 42, no 1, pp 619–622.
[25] Hocken, R.J and Machine Tool Task Force (1980) Technology of Machine Tools, UCRL-52960-5,
Lawrence Livermore National Laboratory, University of California, Livermore, CA
[26] Wang, W.P and Wang, K.K (1986) Geometric modeling for swept volume of moving solids IEEE Comput Graphics Appl., vol 6, no 12, pp 8–17.
Trang 511 Design of Robotic End
Effectors
Hodge Jenkins
Mercer University
11.1 Introduction 11.2 Process and Environment
System Design • Special Environments
11.3 Robot Attachment and Payload Capacity
Integrated End Effector Attachment • Attachment Precision
• Special End Effector Locations • Wrist Compliance: Remote Compliance Centers • Payloads • Payload Force Analysis
11.4 Power Sources
Compressed Air • Vacuum • Hydraulic Fluid Power
• Electrical Power • Other Actuators
11.5 Gripper Kinematics
Parallel Axis/Linear Motion Jaws • Pivoting/Rotary Action Jaws • Four-Bar Linkage Jaws • Multiple Jaw/Chuck Style
• Articulating Fingers • Multi-Component End Effectors
11.6 Grasping Modes, Forces, and Stability
Grasping Stability • Friction and Grasping Forces
11.7 Design Guidelines for Grippers and Jaws
Gripper and Jaw Design Geometry • Gripper Design Procedure • Gripper Design: Case Study • Gripper Jaw Design Algorithms • Interchangeable End Effectors
• Special Purpose End Effectors/Complementary Tools
11.8 Sensors and Control Considerations
Proximity Sensors • Collision Sensors • Tactile Feedback/Force Sensing • Acceleration Control for Payload Limits • Tactile Force Control
11.9 Conclusion
11.1 Introduction
Aside from the robot itself, the most critical device in a robotic automation system is the end effector Basic grasping end effector forms are referred to as grippers Designs for end effectors are as numerous
as the applications employing robots End effectors can be part of the robot’s integral design or added-on
to the base robot The design depends on the particular robot being implemented, objects to be grasped, tasks to be performed, and the robot work environment
This chapter outlines many of the design and selection decisions of robotic end effectors First, process and environment considerations are discussed Robot considerations including power, joint compliance, payload capacity, and attachment are presented Sections reviewing basic end effector styles and design
Trang 612 Sensors and Actuators
Jeanne Sullivan Falcon
National Instruments
12.1 Encoders
Rotary and Linear Incremental Encoders • Tachometer
• Quadrature Encoders • Absolute Encoders
12.2 Analog Sensors
Analog Displacement Sensors • Strain • Force and Torque
• Acceleration
12.3 Digital Sensors
Switches as Digital Sensors • Noncontact Digital Sensors
• Solid State Output • Common Uses for Digital Sensors
12.4 Vision 12.5 Actuators
Electromagnetic Actuators • Fluid Power Actuators
12.1 Encoders
12.1.1 Rotary and Linear Incremental Encoders
Incremental encoders are the most common feedback devices for robotic systems They typically output digital pulses at TTL levels Rotary encoders are used to measure the angular position and direction of a motor or mechanical drive shaft Linear encoders measure linear position and direction They are often used in linear stages or in linear motors In addition to position and direction of motion, velocity can also
be derived from either rotary or linear encoder signals
In a rotary incremental encoder, a glass or metal disk is attached to a motor or mechanical drive shaft The disk has a pattern of opaque and transparent sectors known as a code track A light source is placed
on one side of the disk and a photodetector is placed on the other side As the disk rotates with the motor shaft, the code track interrupts the light emitted onto the photodetector, generating a digital signal output (Figure 12.1)
The number of opaque/transparent sector pairs, also known as line pairs, on the code track corresponds
to the number of cycles the encoder will output per revolution The number of cycles per revolution (CPR) defines the base resolution of the encoder
12.1.2 Tachometer
An incremental encoder with a single photodetector is known as a tachometer encoder The frequency
of the output pulses is used to indicate the rotational speed of the shaft However, the output of the single-channel encoder cannot give any indication of direction
Trang 7is determined by the position of the core within the tube The magnitude of the output of the signal is a function of the distance of the core from the primary coil, and the phase of the output signal is a function
of the direction of the core from the primary coil — towards one secondary coil or the other as shown in the figure
LVDT sensors can be used in applications with large travel requirements However, mechanical alignment along the direction of travel is important for this type of sensor
12.2.1.3 Resolvers
A resolver is essentially a rotary transformer that can provide absolute position information over one revo-lution The resolver consists of a primary winding located on the rotor shaft and a two secondary windings located on the stator The secondary windings are oriented 90◦relative to each other Energy is applied to the primary winding on the rotor As the rotor moves, the output energy of the secondary windings varies sinusoidally Resolvers are an alternative to encoders for joint feedback in robotic applications
12.2.1.4 Inductive (Eddy Current)
Inductive sensors are noncontact sensors and can sense the displacement of metallic (both ferrous and nonferrous) targets The most common type of inductive sensor used in robotics is the eddy current sensor The sensor typically consists of two coils of wire: an active coil and a balance coil, with both driven with a high frequency alternating current When a metallic target is placed near the active sensor coil, the magnetic field from the active coil induces eddy currents in the target material The eddy currents are closed loops
of current and thus create their own magnetic field This field causes the impedance of the active coil to change The active coil and balance coil are both included in a bridge circuit The impedance change of the active coil can be detected by measuring the imbalance in the bridge circuit Thus, the output of the sensor is dependent upon the displacement of the target relative to the face of the sensor coil
The effective depth of the eddy currents in the target material,δ, is given by
δ = 1
π f µσ where f is the excitation frequency of the coil, µ is the magnetic permeability of the target material, and
σ is the conductivity of the target material In order to ensure adequate measurement, the target material
must be three times as thick as the effective depth of the eddy currents
In general, the linear measurement range for inductive sensors is approximately 30% of the sensor active coil diameter The target area must be at least as large as the surface area of the sensor probe It is possible to use curved targets, but their diameter should be three to four times the diameter of the sensor probe In addition, the sensor signal is weaker for ferrous target materials compared with nonferrous target materials This can lead to a reduced measurement range and so this should be investigated with the sensor manufacturer
Inductive sensors can sense through nonmetallic objects or nonmetallic contamination However, if measurement of a nonmetallic target displacement is required, then a segment of metallic material must
be attached to the target
12.2.1.5 Capacitive
Capacitive displacement sensors are another type of noncontact sensor and are capable of directly sensing both metallic and nonmetallic targets These sensors are designed using parallel plate capacitors The capacitance is given by
C =ε r ε0A d
whereε ris the relative permittivity (dielectric constant) of the material between the plates,ε0is the absolute
permittivity of free space, A is the overlapping area between the plates, and d is the distance between the
plates
Trang 812-6 Robotics and Automation Handbook
d
A
sensor plate sensor plate
target target
FIGURE 12.6 Distance and area variation in capacitive sensor measurement.
In displacement sensor designs, a capacitive sensor typically incorporates one of the capacitor plates within its housing and the target forms the other plate of the capacitor The sensor then operates on the
principle that the measured capacitance is affected by variation in the distance d or the overlapping area A
between the plates The capacitance is measured by detecting changes in an oscillatory circuit that includes the capacitor Figure 12.6 shows the distance and area variation methods for capacitive displacement measurement
For detection of nonmetallic targets, a stationary metallic reference is used as the external capacitor plate The presence of the nonmetallic target in the gap between the sensor and the stationary metallic reference will change the permittivity and thus affect the measured capacitance The capacitance will be determined
by the thickness and location of the nonmetallic target Figure 12.7 shows the dielectric variation approach for capacitive displacement measurement
In general, the linear measurement range for capacitive sensors is approximately 25% of the sensor diameter The target should be 30% larger than the sensor diameter for optimum performance In addition, environmental contamination can change the dielectric constant between the sensor and the target, thus reducing measurement accuracy
12.2.1.6 Optical Sensors
Optical sensors provide another means of noncontact displacement measurement There are several types which are commonly used in robotics: optical triangulation, optical time-of-flight, and photoelectric
12.2.1.6.1 Optical Triangulation
Optical triangulation sensors use a light emitter, either a laser or an LED, in combination with a light receiver to sense the position of objects Both the emitter and receiver are contained in the same housing
as shown inFigure 12.8.The emitter directs light waves toward a target These are reflected off the target, through a lens, to the receiver The location of the incident light on the receiver is used to determine the position of the target in relation to the sensor face The type of receiver used may be a position sensitive detector (PSD) or a pixelized array device such as a charge coupled device (CCD) The PSD receiver generates a single analog output and has a faster response time than the output pixelized array device because less post-processing is required It is also typically smaller so that the overall sensor size will be smaller Pixelized array devices, however, are useful when the surface of the target is irregular or transparent
non-metallic target metallic reference
sensor plate
C
FIGURE 12.7 Dielectric variation in capacitive sensor measurement.