Inversions Of Four Bar or Quadratic Kinematic Chain

Inversions Of Four Bar or Quadratic Kinematic Chain

 1. Kinematics
Kinematics studies the geometric properties of the motion of points without regard to their masses or to the forces acting on them. A set of points with the property that the distances between any two of them never varies is called a rigid body or rigid link. The position of a rigid body in space is defined by six dimensions, three translations and three rotations. A kinematic chain is a set of links connected by joints that constrain their relative movement. An open chain is a set of links (such as a common industrial robot) with one end attached to a rigid base . A closed chain may be attached to a rigid base in more than one place. A single loop closed chain attached at each end is commonly called a mechanism.

The state of a mechanism is the set of properties needed to completely determine the positions of all of its constituent parts. These properties are called independent state variables, and their count determines a mechanism's degrees of freedom. Constraints are limitations on the motion of a mechanism or of its constituent parts. A number of dependent variables may be required to determine the relative positions of a mechanism's parts, and they are derived from the independent variables and the external constraints. A determinate mechanism has the property that the number of dependent variables is equal to the number of external constraint conditions.

The links of a planar mechanism are constrained to move in a plane parallel to a base plane, usually by hinged joints whose axes lie perpendicular to the base plane. The axes of hinged joints of a spherical mechanism all intersect at a point. Joints of spatial mechanisms have no special relationship to a common point or

2. The Scene Graph

The scene graph is the emergent object-oriented hierarchical data structure for describing geometric relationships, appearance, and behavior in computer generated virtual reality worlds. It is an acyclic tree, meaning that each branch has a single attachment point, and therefore, it cannot form closed loops. The Java 3D API Specification [3] describes the construction of the scene graph tree , which uses BranchGroup nodes and TransformGroup nodes to connect the branches and uses Leaf Nodes to contain information such as geometric shapes, appearance, lighting, and behavior.

Throughout, this paper uses a particular example from classical mechanics to illustrate the general methods. The four bar linkage, a particular class of planar, determinate, single loop closed kinematic chains, has been the focus of study by mathematicians, philosophers, royalty and engineers for centuries, and, respecting tradition, this paper will employ it as the concrete example. The following describes how the scene graph can be used to describe its geometry and connectivity.

Figure 1 shows a common configuration of a four bar linkage. Rigid links AB, BC, CD, DA are connected by hinged joints (A, B, C, D); one of the links (DA) is considered to be fixed to a foundation, one link is considered to be a driver or input link (AB), the adjacent link is a connector or drag link (BC), and the last, the driven link or the output. (CD).

Figure 2 shows how a scene graph could be used to represent the geometric arrangement of the links of a four bar linkage. The Shape Leaf Nodes represent the geometries and visual properties of the individual links themselves, the Branch and Transform Group Nodes describe the structure of the tree that defines the geometric relationship between them, and the Behavior Leaf Node gives motivation to the input link AB.

The central failings of the bare scene graph are apparent from the figure. While the Behavior node can set the transformation for joint A by setting the independent variable angle_A, and the lengths of the rigid links ab, bc, and cd determine the translations, the rotations at joints B and C are unknown, and the requirement that the 'D' end of the link CD engage the joint D fixed on the base remains unexpressed on the tree's acyclic topology.

3.APPROACH

This section describes a three-pronged approach to using inverse kinematics for solving external constraints on an animated mechanism model in Java 3D™. The first sub-section describes the mathematical background, the solution sequence, and the organization of the scene graph model, the second describes the approach to creating a Constraint class to organize and expedite geometric calculations in support of the solution, and the third sub-section describes the standard way that simple Java 3D™ models are animated, the inherent problems, and an approach to modifications necessary to permit stable and efficient computation.

Solving External Constraints

Typically, constraints can be expressed in a number of equations or inequalities that describe the relationship among machine parts or between machine parts and the foundation. This paper considers a subset of constraints that can be expressed in equations whose terms are time-independent. The example has constraints that set displacements of a mechanism part equal to zero relative to a fixed foundation point. Further, the determinate mechanism discussed in this paper has an equal number of dependent variables that can be set to satisfy those equations. The mathematical problem then reduces to solving N nonlinear equations in N unknowns.

Fi (x1, x2, x3, … xN) = 0 i = 1…N (1)

where F is a function of x, the dependent variables. For very simple mechanisms, the equations can be solved from quadratic or trigonometric closed forms, but numerical marching techniques are preferable for mechanisms of any complexity.

Press et al. [2] describe the Newton-Raphson method, simplest of the numerical techniques for solving sets of simultaneous nonlinear equations. The method begins with an initial guess for the dependent variables (xj), measures the resulting values of the functions F, calculates and applies a change to the dependent variables and repeats to convergence.

In the general case, the equation set (1) can be particularly troublesome when it represents kinematic constraints, because it may have many, one, or no solutions. According to Press, there are no good methods to find global solutions to the set, and accordingly, the methods described here are applicable only to mechanisms for which there are known solutions and only to stable regions for those mechanisms.

The key to stability and rapid convergence is an initial guess not too far from the final result. The changes required to the dependent variables are estimated by estimating the local derivatives of Fi with respect to xj, then using them to compute the new xj required to drive Fi to zero. The derivatives Fi/xj are measured by incrementing each xj in turn and measuring the changes to F. The NN matrix Fi/xj is called the Jacobian, J. In vector form:

F (x + x) = F (x) + J x + (higher order terms) (2)

Setting F (x + x) = 0 to satisfy the constraint equations, and neglecting higher order terms

J x = -F (xold),

which is a set of N linear equations in N unknowns. It may be solved for x by one of several different methods, such as direct inversion of the Jacobian

xnew = xold + x

xnew = xold + J-1 (-F (xold)), (3)

and the steps are repeated until F (xold) are sufficiently close to 0. For a high fidelity simulation, this procedure is executed and the dependent variables are set prior to the rendering of each frame.

A Simple Guide to Dimensions ...

This drawing (shown to the left) is symmetric about the horizontal centre-line.

Centre-lines are chain-dotted and are used for symmetric objects, and also for showing the centre of circles and holes.
Drawing dimensions should generally be done directly to the centre-line, as shown on the left. In many cases this method
can be clearer than just dimensioning
between surfaces.

Note again that the measurements show only numbers. The statement at the bottom of the drawing identifies that these numbers are the dimensions in Millimetres.

A Simple Guide to Dimensions

A Simple Guide to Dimensions

 

With the left side of the block composed solely of "radiuses" (radii) - as shown here, we break our rule that we should not duplicate dimensions. The total length is known because the radius of the curve on the left side is given. Then, for clarity, we add the overall length of 60 and we note that it is a reference (REF) dimension.
This means that it is not really required.

Somewhere on the paper, usually the bottom, there should be placed information on what measuring system is being used (e.g. inches and millimetres) and also the scale of the drawing.

“Assembly" Drawings

                                                   “Assembly" Drawings

1An isometric view of an "assembled" pillow-block bearing system is shown on the left below. 
It corresponds closely to what you actually see when viewing the object from a particular
angle. We cannot tell what the inside of the part looks like from this view.

                                                                                                         

We can also show isometric views of the pillow-block being taken apart or disassembled"
(above – right). This allows you to see the inner components of the bearing system.
Isometric drawings can show overall arrangement clearly, but not the details and the dimensions.


"Cross-Sectional Views"

A cross-sectional view portrays a cut-away portion of the object and is another way to show hidden components in a device. Imagine a plane that cuts vertically through the centre of the pillow block as shown in figure 12. Then imagine removing the material from the front of this plane, as shown in figure 13.

This is how the remaining rear section would look. Diagonal lines (cross-hatches)
show regions where materials have been cut by the cutting plane.
This cross-sectional view (section A-A, figure 14), one
that is ‘orthogonal’ to the
viewing direction, shows the relationships of lengths and
diameters in a much better way. These drawings are easier to make than isometric drawings. Experienced engineers can interpret orthogonal drawings without needing an isometric drawing, but this can take a bit of practice.

The top "outside" view of the bearing is shown in figure 15. It is an orthogonal perpendicular) projection.* Notice the direction of the arrows for the "A-A" cutting plane

Drawing Tools

To prepare a drawing, you can use manual drafting instruments (see below) or computer-aided drafting or design. ( CAD ) The basic drawing standards and conventions are the same regardless of what design tool you use to make the drawings. In learning ‘drafting‘ - the name given to drawing in architecture and engineering, we will approach it from the perspective of manual drafting. If the drawing is made without either instruments or CAD, it is called a freehand sketch.



It is important to use the set-square resting on the parallel motion bar - the horizontal motion bar - as
the accuracy of the lines drawn and the speed with which they can be added is significantly improved. Isometric drawings need the 30 / 60 set sqaure and Orthographics use the 45 / 90 degree. Always use a sharp pencil as the line is more accurate and can be mesured more easily. HB is the softest grade of pencil that should be used. Either H or 2H grades give lighter-looking lines but are far finer and cleaner looking.

A moments thought will also make you realise that unless the paper is attached to the surface with its edges aligned to the board - then the drawing will not be square to the edge and nor will replacing the drawing be quite as easy if for some reason it has to be removed and replaced later. Steel clips or masking tape can be used to attach the paper to the board’s surface. When peeling tape off drawings make sure it is pulled back almost along itself so that the paper surface is not damaged.

ISOMETRIC

ISOMETRIC (2 angles) TRIMETRIC (3 angles)
In Isometric drawings try to get used to ‘flipping’ the set-square over keeping the longest edge in contact with the horizontal motion bar.
Always keeping the ‘sharpest’ (narrow angle) part pointing either left or right. Only when a 90 degree angle is needed can the sharpest (narrow) angle of the set-square point to the top of the page. Trimetric drawing uses 3 angles.

Isometric Drawing

           "Engineering Drawing and Sketching"

• 1 Isometric Drawing info

               One of the best ways to communicate one's ideas is through some form of picture or drawing. This is especially true for the engineer.
The purpose of this guide is to give you the basics of engineering sketching and drawing.

We will treat "sketching" and "drawing" as one. "Sketching" generally means freehand drawing. "Drawing" usually means using drawing instruments, from compasses to computers to bring precision to the drawings. As this is just an introduction, don't worry about understanding every detail immediately - just get a general feel for the language of graphics and drawings. Before starting on any technical drawings, let's get a good look at this block drawing, shown below, from several angles. Any engineering drawing should show everything - a complete understanding of the object should be possible from the drawing without any need for explanations. If the isometric drawing can show all details and all dimensions on one drawing, it is ideal.





                                               "2 Isometric Drawing sempal"

The representation of the object seen
here is called an isometric drawing.
This is one of a family of three-dimensional views called pictorial drawings. In an
isometric drawing, the object's vertical
lines are drawn vertically, and the
horizontal lines in the width and depth planes are shown at 30 degrees to the horizontal.
When drawn under these guidelines, the
lines parallel to these three axes are at
their true (scale) lengths. Lines that are
not parallel to these axes will not be of
their true length.

Further reading

Y14.100–2004 Engineering drawing practices
Y14.24–1999 Types and applications of engineering drawings
Y14.3–2003 Multiview and sectional view drawings
Y14.31–2008 Undimensioned drawings
Y14.36M–1996 Surface texture symbols
Y14.38–2007 Abbreviations and acronyms for use on drawings and related documents
Y14.4M–1989 Pictorial drawing
Y14.41–2003 Digital product definition data practices
Y14.42–2002 Digital approval systems
Y14.5–2009 Dimensioning and tolerancing
Y14.5.1M–1994 Mathematical definition of dimensioning and tolerancing principles
Y14.6–2001 Screw thread representation
Y32.7–1972 Graphics symbols for railroad maps and profiles

Engineering drawing abbreviations and symbols

                                                   THE ENGINEERING DRAWING
Engineering_drawing_abbreviations_and_symbols



Engineering drawing abbreviations and symbols


Engineering drawing abbreviations and symbols are used to communicate and detail the characteristics of an engineering drawing.

Technical standards exist to provide glossaries of abbreviations, acronyms, and symbols that may be found on engineering drawings. Many corporations have such standards, which define some terms and symbols specific to them; on the national and international level, ASME standard Y14.38[1] is probably the most widely used.

A
AC[2] across corners Commonly used when measuring the corners of a hex drive, such as a hex nut.
AF[2] across flats Commonly used when measuring the corners of a hex drive, such as a hex nut.
Al or AL aluminium
ALY alloy
AMER American
AMS Aerospace Material Standards Standards in materials science and engineering maintained by SAE International and widely used in the aerospace manufacturing industries.
AN- Army-Navy A prefix for standard hardware (catalog hardware) ID numbers. Came from the era of circa 1890s-1945, when the U.S. Army and Navy were leading the way on product standardization for logistics improvement, yielding the United States Military Standards system. Today industry and ISO also do a lot of this standardization specification, freeing the U.S. DoD and military to do less of it (as explained at United States Military Standard > Origins and evolution), although many MIL standards are सतill current. (See also MS- and NAS.)
ANN anneal, अनnealed
ANSI American National Standards Institute And the many standards that it issues, for example, ANSI Z87.1.
APPROX[3] अपproximately
AQL अच्सप्ताब्ले quality level The threshold of defectiveness that is allowable in a group of parts. It is trivial to say थाt no one wants any error, and that everyone wants uniform perfection; but in the real world, it almost never happens. The intelligence behind defining AQLs is in figuring out how much error is तोलेराब्ले given the costs incurred or not incurred.
AS Aerospace सतandards Standards maintained by SAE International and widely used in the aerospace manufacturing इndustries. Standard aerospace hardware sometimes has the AS- prefix in the catalog numbers.
AS, APS, APV, AV, APSL, AVL approved product supplier, approved vendor, approved-product-supplier list, अप्पroved-vendor list When only certain companies are approved by the CDA to manufacture थे product (that is, to make what the drawing depicts/defines), they are called by names such as "अप्प्रोवed supplier", "approved product supplier", "approved vendor", or "approved product vendor". The list of such companies (which usually changes over time) is called an APSL, AVL, or similar names. Vetting the companies on this list requires the CDA to audit (and possibly periodically re-audit) the companies, which incurs an overhead expense for the CDA. Therefore, smaller companies will often cite larger companies' lists in order to avoid the cost of duplicating the effort.
ASA American Standards Association Former name for ANSI (1920s-1960s).
ASME अमेरिकेन Society of Mechanical Engineers And the many standards that it issues, for example, ASME Y14.5.
ASSY or ASY असembly referring to an assembly of parts rather than just one (sub)part ("piece part", "detail part").
ASTM Formerly the American Society for Testing and Materials; now ASTM International Maintains technical स्तंदाrds, especially regarding materials science and engineering and metrology.
AVG average
AWG American Wire Gauge


बी
BASIC basic दिमension A basic dimension is one that is the theoretical value without any tolerance range. It does not serve as an acceptance criterion. It is thus similar in some respects to a reference dimension. The reason why a basic dimension does not carry a tolerance is that its actual value will fall (acceptably) wherever it is put by other features' actual values, where the latter features are the ones with tolerances defined. In modern practice basic dimensions have a rectangular box around them, or sometimes the word "BASIC".
BC or B.C. bolt circle
BHN Brinell hardness number
BoM or BOM bill of materials Also called a list of materials (LM or L/M). Overlaps a lot in concept with a parts list (PL or P/L). There is no consistently enforced distinction between an L/M, a BoM, or a P/L.
BRZ bronze




C
CAD computer-aided design, computer-aided drafting; cadmium [plating]
CAGE Commercial and Government Entity [code] A CAGE code is a unique identifier to label an entity (that is, a specific government agency or corporation at a specific site) that is a CDA, ODA, or MFR of the part defined by the drawing. One corporation can have many CAGE codes, as can one government, because each division, department, and site (campus) can have its own CAGE code. The same CAGE code can change owners over the years. For example, a CAGE code that formerly referred to a certain Martin Marietta site will now refer to Lockheed Martin at that same site (although the buildings may have been replaced and the signage may say different names).
C-C or C-TO-C centre-to-centre; on centres Defines centre-to-centre distance of two features, such as two holes.
CBN cubic boron nitride A material from which some cutter inserts are made.
CDA current design activity The CDA is the entity (whether it be a corporation, a unit of a national military or ministry of defence, or another civilian government agency) that currently has design authority over the part design (definition). It may be the entity who first designed the part (that is, the ODA), but today it is also likely to be a designated successor entity, owing to mergers and acquisitions (M&A) activity (e.g., ODA company was bought by CDA company); contract letting (e.g., an Army engineering department ODA turns over the design activity to the prime contractor that makes most or all of the parts, turning that contractor into the new CDA); privatization (e.g., a government privatizes the design and manufacture of materiel, and a state arsenal [state armory] ODA transfers design authority to a private armory [defense contractor] ODA); or patent licensing (e.g., a patent-holding inventor [ODA] licenses one or several companies to manufacture products using his intellectual property, in which case the "same" part could end up with multiple design authorities, although they may not be considered the official/nominal CDA).
CERT or cert certification For example, certification of metallurgical content and processes
CG centerless ground, centerless grinding
CL or ℄ center line Center line of a feature
Center mark Defines the center of a circle or partial circle.
CHAM chamfer
CI cast iron
CNC computer numerical control
CR controlled radius Radius of an arc or circle, with no flats or reversals. This strict version of radius definition is specified in demanding applications when the form of the radius must be controlled more strictly than "just falling within the dimensional tolerance zone". It is poor engineering to specify a CR instead of an R simply on the theory of enforcing good workmanship. CR is for critical features whose performance truly requires near-perfect geometry. Like most such characteristics, its presence increases the price of the part, because it raises the costs of manufacturing and quality assurance.
CRES corrosion-resistant [steel] Largely synonymous with stainless steel, unless specific grades, specs, and distinctions are made on the drawing. Some people treat CRES as a subset of the stainless steels.
CRS cold rolled steel; on centres Defines centre-to-centre distance of two features, such as two holes.
C'BORE or CBORE or counterbore
CSK or CSINK or countersink
CTN, ctn carton




D
depth, deep, down Defines the depth of a feature.
D or ⌀ or DIA[3] diameter Diameter of a circle. In a feature control frame (FCF), the ⌀ symbol tells you that the tolerance zone for the geometric tolerance is cylindrical.
DIM dimension, dimensioning
DoD, DOD [U.S.] Department of Defense See also MoD.
DPD digital product definition A synonym of MBD.




E
EO, ECO, ECN engineering order An order from the engineering department (to be followed by the production department or vendor) overriding/superseding a detail on the drawing, which gets superseded with revised information. Also called by various other names, such as engineering change order (ECO), engineering change notice (ECN), drawing change notice (DCN), and so on. See also REV.
EQ equal, equally For example, "⌀10 4X EQ SPACED ON BC" means "drill four holes of 10mm diameter equally spaced around the bolt circle."




F
f finish An italic f (Latin small letter f) written on a line representing a surface was an old way of indicating that the surface was to be machined rather than left in the as-cast or as-forged state. The "f" came from "finish" in the sense of "machine finish" as opposed to raw stock/casting/forging. Later the ASA convened upon a letter V (specifically a sans-serif V) touching the surface. Soon this evolved into the "check mark" sign with accompanying number that tells the reader a max roughness value (RMS, microinches or micrometres) for the machined finish, to be measured with a profilometer.
FAO finish all over A note telling the manufacturer that all surfaces of the part are to be machined (as opposed to leaving any surfaces as-cast or as-forged). Not an obsolete usage, but not seen as commonly as it was decades ago; not least because parts that once would have been spot-faced castings are now likelier to be contoured from billet with CNC milling. But more importantly, best engineering practice today, reflecting design for manufacturability and avoidance of spurious cost drivers, is either to specify specific, quantifiable requirements for surfaces with specific needs (such as RMS roughness measurements in microinches or micrometres, plus any plating or painting needs), or to leave finish out of the part definition (and thus at the manufacturer's discretion) because it is not important to fit, function, or criticality. This same spirit is behind the shift in military standards from writing requirements about methods to writing them instead about performance, with the method to reach that goal being up to the ingenuity of the designer.
FCF feature control frame The rectangular box (with several cells) that conveys geometric tolerances in GD&T. It typically tells you what sort of geometric condition (e.g., parallel, perpendicular, round, concentric), followed by what size (and maybe shape) the tolerance zone is, and finally which datums it relates to, the order of gaging against them, and what material condition applies to them (LMC, MMC, or RFS). A diameter symbol (⌀) tells you that the zone for the geometric tolerance is cylindrical.
FD or F/D field of the drawing The [main] field of the drawing, as opposed to other areas of it, such as the parts list (P/L), general notes (G/N), flagnotes (F/N or FL), title block (T/B), rev block (R/B), bill of materials (B/M or BoM or BOM), or list of materials (L/M). Rationales for drawing changes that are noted in the rev block often use these abbreviations for brevity (e.g., "DIM 14 was 12; added default TOL info to T/B; added leader lines to F/D; added alternate hardware IDs to P/L; added alternate alloy to L/M").
FL flag note, flagnote A note that is called out in specific spots in the field of the drawing. It is numbered with a stylized flag symbol surrounding the number. A general note applies generally and is not called out with flags.
FN or F/N flag note, flagnote A note that is called out in specific spots in the field of the drawing. It is numbered with a stylized flag symbol surrounding the number. A general note applies generally and is not called out with flags.
FoS feature of size A type of physical feature on a part. An FoS is a feature that can have size associated with it, usually involving the opposition of two surfaces (e.g., the two diametrically opposite sides of a hole wall; the two opposite walls of a slot or flange). Features of size (FoSs) in reality always have actual sizes and forms that differ from their theoretical size and form; the purpose of tolerancing is to define whether the difference is acceptable or not. Thus material condition (LMC, MMC, somewhere in between, or RFS) is important in GD&T. ) A given geometric tolerance may be defined in relation to a certain FoS datum being at LMC or at MMC.
FSCM Federal Stock/Supply Code for Manufacturers An older name for "CAGE code". Also NSCM (National Stock/Supply Code for Manufacturers).




G
GCI gray cast iron
GD&T or GDT geometric dimensioning and tolerancing A standardized language for defining and communicating dimensions and tolerances.
GN or G/N general note(s) Most engineering drawings have a notes list, which includes both general notes and flag notes.
H
HBW hardness, Brinell, tungsten tip See Brinell scale. (The "W" comes from the element symbol for tungsten, W, which comes from the German Wolfram.)
HRA hardness, Rockwell, A scale See Rockwell scale.
HRB hardness, Rockwell, B scale See Rockwell scale.
HRC hardness, Rockwell, C scale See Rockwell scale.
HRS hot rolled steel
HT TR heat treat, heat treatment
H&T or H/T or HT hardened and tempered A form of heat treatment in which the metal is first hardened and then tempered. Compare N&T.




I
IAW in accordance with A common need in engineering drawings is to instruct the user to do activity X in accordance with technical standard Y. For example, "Weld all subassemblies IAW AWS XYZ.123" means "Weld all subassemblies in accordance with American Welding Society standard number XYZ.123" (the number is hypothetical in this example). The word "per" is functionally equivalent to "IAW" in such contexts; thus "rivet all sheet metal per MIL-PRF-123456" or "[...] IAW MIL-PRF-123456". Part of the motivation behind the choice of words "in accordance with" is that they do not allege that any particular activity is explicitly specified by standard XYZ.123 (which "per" could be interpreted as alleging, at least in connotation); rather, these words merely instruct the user that whatever s/he does must not contradict the standard in any way. But this is a subtle connotative distinction, and "per" and "IAW" are denotatively equivalent.
ID inner diameter; identity, identification number
ISO International Organization for Standardization And the many standards that it specifies, for example, ISO 10303





K 
कसI, ksi kilopounds per square inch, that is, thousands of pounds per square inch KSI (or ksi) is a सीओmmon non-SI measurement scale for ultimate tensile strength, that is, the number of units of तेंsile force that a material can endure per unit of cross-sectional area before breaking. In the SI system, the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the mega- prefix); or, equivalently to pascals, newtons per square metre (N/m²).


L
LH left-hand Referring to handedness, such as the helix handedness of screw threads or the mirror-image handedness of a symmetrical pair of parts.
LM or L/M list of materials Also called a bill of materials (BoM, BOM). Overlaps a lot in concept with a parts list (PL or P/L). There is no consistently enforced distinction between an L/M, a BoM, or a P/L.
LMC least material condition A material condition in GD&T. Means that a feature of size (FoS) is at the limit of its size tolerance in the direction that leaves the least material left on the part. Thus an internal feature of size (e.g., a hole) at its biggest diameter, or an external feature of size (e.g., a flange) at its smallest thickness. The GD&T symbol for LMC is a circled L. (See also MMC and RFS.) A given geometric tolerance may be defined in relation to a certain FoS datum being at LMC or at MMC.


M
MACH machine; machined
MAX[3] maximum
MBD model-based definition Definition of the part via a 3D CAD model rather than via a 2D engineering drawing. Drawings may be printed (plotted) from the model for reference use, but the model remains the governing legal instrument.
MFD manufactured
MFG manufacturing
MFR manufacturer May be the same entity as the CDA or ODA, or may not be.
MIL- [U.S.] Military A prefix for the names of various United States Military Standards and Specifications, for example, MIL-STD-*, MIL-SPEC-*, MIL-DTL-*, MIL-PRF-*, MIL-A-*, MIL-C-*, MIL-S-*, MIL-STD-1913, MIL-STD-1397.
MIN[3] minimum; minutes
MMC maximum material condition A material condition in GD&T. Means that a feature of size (FoS) is at the limit of its size tolerance in the direction that leaves the most material left on the part. Thus an internal feature of size (e.g., a hole) at its smallest diameter, or an external feature of size (e.g., a flange) at its biggest thickness. The GD&T symbol for MMC is a circled M. (See also LMC and RFS.) A given geometric tolerance may be defined in relation to a certain FoS datum being at LMC or at MMC.
MoD, MOD Ministry of Defence [U.K. and others] See also DoD.
MPa, MPA megapascals The common SI measurement scale for ultimate tensile strength (UTS), that is, the number of units of tensile force that a material can endure per unit of cross-sectional area before breaking. There is only one correct casing for the symbol, cap-M-cap-P-small-a, which, like any SI unit of measurement symbol, properly should be preserved even when surrounding text is styled in all caps (which latter is a frequently employed tradition in engineering drawing). But it is not uncommon to see "MPA" through carelessness. Users are not confused regardless. In non-SI terms, the unit for UTS is the KSI (or ksi), which see herein.
MS- [U.S.] Military Standard Standards established by the U.S. military and widely used in the aerospace manufacturing (military and civil) and other defense industries. Standard hardware sometimes uses the MS- prefix in the catalog numbers. (See also AN- and NAS.)


N
NOM[3] nominal
NORM or NORMD normalized referring to normalization, a stress-relieving heat treatment. See also HT TR.
NAS National Aerospace Standards Standards maintained by SAE International and widely used in the aerospace manufacturing industries. The "National" formerly implicitly referenced the USA, but today NAS and other standards are used globally. Standard hardware for aerospace work sometimes uses the NAS- prefix in the catalog numbers. (See also AN- and MS-.)
NC National Coarse; numerical control The [U.S.] National Coarse series of pre-1949 corresponds today to the Unified National Coarse (UNC) of the Unified Thread Standard.
NEF National Extra Fine The [U.S.] National Extra Fine series of pre-1949 corresponds today to the Unified National Extra Fine (UNEF) of the Unified Thread Standard.
NF National Fine The [U.S.] National Fine series of pre-1949 corresponds today to the Unified National Fine (UNF) of the Unified Thread Standard.
NL or N/L notes list A list of notes that appears somewhere on the drawing, often in the upper left corner.
NPS National Pipe Straight A subset series of the Unified Thread Standard.
NPT National Pipe Taper A subset series of the Unified Thread Standard.
NS National Special A screw thread series; see Unified Thread Standard. An extensible series, covering various special threads.
NSCM National Stock/Supply Code for Manufacturers An older name for "CAGE code". Also FSCM (Federal Stock/Supply Code for Manufacturers).
N&T or N/T or NT normalized and tempered A form of heat treatment in which the metal is first normalized (stress-relieved) and then tempered. Compare H&T.
NTS not to scale See also Engineering drawing > Scale.


O
OAL overall length
OC on center(s) That is, centre-to-centre; defines centre-to-centre distance of two features, such as two holes.
OD outer diameter
ODA original design activity The entity that originally designed a part. Compare to CDA, the entity that currently has design authority over the part design (definition).
ORIG original


P
pc, pcs piece, pieces
PD pitch diameter
PDM, PDMS product data management, product data manager [app], product data management system [app] A database(s) and related application(s) that facilitate all aspects of managing data files—e.g., TDPs, TDP versions, drawings, model datasets, specs, addenda, certs, memoranda, EOs, ECOs, DCNs, RFQs, quotes, POs, e-mails, faxes, photos, word processor documents, spreadsheets. See also PLM.
PH precipitation hardening, precipitation-hardened
PHR BRZ phosphor bronze
PL or P/L parts list A list, usually tabular and often on the drawing (if not accompanying the drawing on a separate sheet), listing the parts needed in an assembly, including subparts, standard parts, and hardware. There is no consistently enforced distinction between an L/M, a BoM, or a P/L.
PLM product lifecycle management; plant lifecycle management See also PDM.
PN or P/N part number
POI or TSC point of intersection or theoretical sharp corner A point that makes the layout of the part easier. It is usually the intersection of the tangent lines of a curve.
PSI pounds per square inch A unit of measurement for pressure. See also KSI.
PTFE polytetrafluoroethylene Also well known by the brand name Teflon.


Q
QMS quality management system A system in place to ensure that quality of manufacture is produced and maintained; a system to prevent defective parts from being made, or, even if made, from getting into finished inventories.


R
R radius Radius of an arc or circle. Flats and reversals (falling within the dimensional tolerance zone) are tolerated unless "CR" (controlled radius) is explicitly specified.
REF or ( )[3] reference The dimension or note is given only for reference and thus is not to be used as a part acceptance criterion (although it may be used as an aid to production or inspection). The dimension may also be surrounded by parentheses to signify a reference dimension. When a dimension is defined in one view but also mentioned again in another view, it will be given as reference in the second case. This rule prevents the mistake of defining it in two different ways accidentally; the "main" (non-reference) mention is the only one that counts as a feature definition and thus as a part acceptance criterion. See also basic dimensions, which are similar in some respects.
REQD or REQ'D required For example, "4 REQD" written next to a fastener means that four of those fasteners are required for the assembly.
REV revision Engineering drawings and material or process specifications are often revised; the usual revision control convention is to label the versions A, B, C, D, etc; a revision block (rev block) is a tabular area on the drawing (typically in the upper right corner) that lists the revision letters, a brief description of the changes and reasons, and approval initials and dates. Revisions beyond "Z" start the alphabet over again with doubling, e.g., AA, AB, AC, AD, and so on. In the days of manual drafting, redrawing was expensive, so engineering orders (EOs, ECOs, DCNs, ECNs) were not always incorporated into a next-letter revision. They thus accompany the drawing as part of the TDP. With the dissemination of software usage (CAD, CAM, PDMSs), revision control is often better handled nowadays, in competent hands at least. In recent years the revision control of engineering drawings has even been standardized by ASME, in their standard Y14.35M.[4]
RFS regardless of feature size A material condition (or more precisely, freedom from such) in GD&T. Means that a given geometric tolerance is true in relation to a certain datum regardless of its actual size (LMC ≤ actual size ≤ MMC).
RH right-hand Referring to handedness, such as the helix handedness of screw threads or the mirror-image handedness of a symmetrical pair of parts.
RMS root mean square RMS in general is a statistical technique to define a representative value for a group of data points. With regard to surface roughness, it means that the heights of the individual microscopic peaks and valleys shall be averaged together via RMS to yield a measurement of roughness. See also herein f as a finish mark.
R/T or RT rough turn, rough turned Turned on a lathe but not finished to a final machined dimension and roughness. Can apply to bar stock or to parts in-process.
RTP release to production The issuance of a drawing from the engineering/design activity to the production activity. In other words, the event when a draft becomes a completed, official document. A stamp on the drawing saying "ISSUED" documents that RTP has occurred.


S
SHCS socket head cap screw A cap screw with a socket head (usually implying a hex socket, driven with a hex key.
SHSS socket head set screw A set screw with a socket head (usually implying a hex socket, driven with a hex key.
SI Système international [d'unités] [International System of Units] The metric system in its current form (latest standards).
SAE Formerly the Society of Automotive Engineers; now SAE International And the many standards that it issues, for example, the SAE AMS and SAE AS standards series.
SN or S/N serial number
SOL ANN solution anneal, solution annealed
SPEC or spec specification
SPOTFACE Spot facing
SR spherical radius Radius of a sphere or spherical segment.
SS stainless steel
SST stainless steel A somewhat unusual abbreviation; spell out for clarity. "SS" or "CRES" are more likely to be recognized with certainty.
STD Standard
STEP Standard for the Exchange of Product Model Data A standard format defined by ISO 10303 for MBD data generation, storage, and exchange.
STA solution treated and aged
STL steel
STK stock A nominal dimension for the stock material, such as bar stock


T
TAP Tapped hole Usually implies drilling a hole if the hole does not already exist.
TB or T/B title block An area of the drawing, almost always at the bottom right, that contains the title of the drawing and other key information. Typical fields in the title block include the drawing title (usually the part name); drawing number (usually the part number); names and/or ID numbers relating to who designed and/or manufactures the part (which involves some complication because design and manufacturing entities for a given part number often change over the years due to mergers and acquisitions, contract letting, privatization, and the buying and selling of intellectual property—see CDA and ODA); company name (see previous comment); initials/signatures of the original draftsman (as wells as the original checker and tracer in the days of manual drafting); initials/signatures of approving managers (issuance/release-to-production information); cross-references to other documents; default tolerancing values for dimensions, geometry, and surface roughness; raw-material info (if not given in a separate list/bill of materials); and access control information (information about who is authorized to possess, view, or share copies of the information encoded by the drawing, e.g., classification notices, copyright notices, patent numbers). Drawing revision (versioning) information is not always included in the title block because it often appears in a separate revisions block.
TDP technical data package The complete package of information that defines a part, of which the drawing itself is often only a subset. It also includes engineering orders (drawing change notices), 3D model datasets, data tables, memoranda, and any special conditions called out by the purchase order or the companies' terms-and-conditions documents.
THD or thd thread
THRU Through Usually applied to a hole dimension to signify that the hole extends through the wall thickness; in other words, a through hole rather than a blind hole
THRU ALL Through all Similar to THRU except the hole extends through the whole workpiece. This is usually used if there are multiple openings that the feature extends through. "THRU" means "through [one] wall"; "THRU ALL" means "through all walls".
Ti titanium
TiN titanium nitride [plating]
TIR total indicated runout; total indicator reading For measurements of eccentricity and other deviations from nominal geometry
TOL tolerance, tolerancing
TYP[3] Typical Other features share the same characteristic. For example, if the drawing shows 8 holes on a bolt circle, and just one is dimensioned, with "TYP" or "(TYP)" following the dimension label, it means that that hole is typical of all 8 holes; in other words, it means that the other 7 holes are that size also. The latest revisions of Y14.5 deprecate "TYP" by itself in favor of the specifying of a number of times, such as "2X" or "8X". This helps avoid any ambiguity or uncertainty.


U
UNC Unified National Coarse A subset series of the Unified Thread Standard.
UNEF Unified National Extra Fine A subset series of the Unified Thread Standard.
UNF Unified National Fine A subset series of the Unified Thread Standard.
UNS Unified National Special; unified numbering system Unified National Special is a subset series of the Unified Thread Standard. It is an extensible series, covering various special threads. The unified numbering system is a vaguely named standard for naming alloys by principal element percentages.
USASI United States of America Standards Institute Former name for ANSI (1966-1969).
USS United States Standard; United States Steel U.S. Standard threads became the National series (e.g., NC, NF, NEF), which became the Unified National series (e.g., UNC, UNF, UNEF); see Unified Thread Standard. As for U.S. Steel, it was once the largest steel company on earth, often an approved supplier, and not infrequently a sole source; hence its mention on drawings.
UTS ultimate tensile strength; Unified Thread Standard


V
v finish A letter v (Latin small letter v) written on a line representing a surface is a way to indicate that the surface is to be machined rather than left in the as-cast or as-forged state. The older symbol for this was a small script (italic) f (see herein f). Later the ASA convened upon a letter V (specifically a sans-serif V) touching the surface. Soon this evolved into the "check mark" sign with accompanying number that tells the reader a max roughness value (RMS, microinches or micrometres) for the machined finish, to be measured with a profilometer.


W
WC tungsten carbide The "W" comes from the element symbol for tungsten, W, which comes from the German Wolfram.
WI wrought iron Both the material and the abbreviation are obsolete, or nearly so. Spell out the words if this material is to be mentioned at all in modern drawings.


X
X[3] or ( ) number of places—for example, 8X or (8) When a dimension is used in multiple places either of these prefixes can be added to the dimension to define how many times this dimension is used. This example signifies eight places. (Note on character encoding: Although in typography (including Unicode) the letter X and the multiplication sign (×) are distinct characters with differing glyphs, it is a longstanding tradition in engineering drawing that the letter X is interchangeable with the multi sign, unless otherwise specified by the CAx systems used.)


Y
Y14.X — Calls out the drawing standard that this drawing is following. For example, ASME Y14.5 and Y14.100 are commonly used standards that define all of the symbols and drafting conventions used.


Z