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Process capability prediction methods for position tolerance under maximum material condition were discussed in this paper. Due to application of maximum material condition the position tolerance specification varied individually for each part, percentage normalization and minimum gap methods were introduced to calculate the position process capability index. Link was taken as an example, true position percentage normalization and minimum gap of 30 parts were calculated. Considering the true position constitution relative to position tolerance at maximum material condition, related individual percentages were used to express the result and the same tolerance size 100% was obtained as for a unilateral tolerance. Set the acceptable value was 0, minimum gap between a hole and a simulated position gauge pin is studied instead of position. The process capability prediction results of two methods were calculated by Minitab software.

This paper focuses on process capability evaluation method for position tolerance under maximum material condition. Due to application of maximum material condition the position tolerance specification varies individually for each part, the approach of percentage normalization is introduced to calculate position process capability index. Bush is taken as an example, and true position percentage normalization of 30 parts are calculated. Considering the true position constitution relative to position tolerance at maximum material condition, related individual percentages are used to express the result and the same tolerance size 100% is obtained as for a unilateral tolerance. Process Capability index is calculated with Minitab software.

Engineering tolerance plays an important role in the process capability analysis for determining whether a manufacturing process is capable of making good quality products. In contrast with the engineering tolerance region in a multivariate manufacturing process, the multidimensional machining process or the nano-cutting process has a special engineering tolerance called the positional tolerance. Positional tolerance is a special type of geometric dimensioning and tolerancing which describes the tolerance region between the actual location of machining results and the target location. In the past few years, several capability indices have been developed for measuring the performance of a multidimensional machining process under the assumption that the variances of machining results on different directions are equal. However, this assumption may not be true in most practical situations. In this paper, we propose three novel capability indices for measuring the performance of a multidimensional machining process under the assumption that the variances of machining results on different directions may not be equal. The statistical properties of the point estimators and their confidence intervals for the new capability indices are derived. Both the simulation results and numerical examples show that the new capability indices outperform the predecessors.

Fixture error is one of the error sources in machining operations. Locator position inaccuracy and locator height error are the main sources of fixture error. The optimal positions of the locators are a critical problem for minimizing the geometrical and dimensional error of workpiece. This article proposes a genetic algorithm–based optimization method to arrive at a layout of locators for minimum machining error in 3-2-1 locating approach. The focus of this optimization is the positional tolerance of holes. So, a mathematical model of the hole position tolerance with respect to variation of locator position is developed. The planes of the workpiece actual coordinate system are mathematically modeled on the workpiece theoretical coordinate system. The capability of the proposed approach has been shown by using an example. The result shows that the proposed genetic algorithm method can be used to calculate locating errors and find the optimal locating layout within the specified tolerance range, which is critical for fixture design in hole-making process.

New methods of data acquisition such as 3D scanners have become increasingly necessary for the verification of the geometric dimensioning and tolerancing (GD&T) specifications in the manufacture of industrial parts. This paper proposes a method for the verification of a positional tolerance in two cylindrical features in an industrial part digitized using a 3D non-contact scanner. Apart from enabling an adequate quantification of the obtained results, this method also permits the displaying of different ways of visualizing the results. The tolerance zone within which the used scanner carries out the analysis was measured and quantified. Some aspects taken into consideration were the geometric quality of the piece and the repeatability, the reproducibility and the uncertainty of the digital process, which comprises the acquisition and processing of the data. This research work concludes that the digital method presented hereby, with its corresponding virtual inspection, is valid for the verification of positional tolerances, even when it is required to maintain the GD&T specification regardless of the feature size. In addition, this article raises the discussion over the best way to compute the traditional datum referencing rules to the new data acquisition methods.

The paper presents the issue of improvement control accuracy details directly on metal cutting machine tools. The paper considers indicators of the accuracy of machine tools, certain ways to increase the accuracy of machine tools, describes the methods of reducing errors. Approaches to metal cutting equipment functional diagnostics are considered, namely the parameters verification of a working body positioning to maintain potential of OMV-technologies on a machine. The research objective is to assess the accuracy of measurement depending on machine dynamics specifically on the probing feed rate and the geometrical accuracy of the machine tool using mathematical statistics methods. The test specimina measurements were performed twice: directly on a machine tool with PowerInspect OMV and on embedded software coordinate measurement machine. The similar test was performed before and after machine setting. The component measurement feed rate on a machine tool was determined to affect the results of measurement, and the deviation rate is less at the feed rate being increased. By reducing the position tolerance by a factor of 2, the measurement accuracy is increased by a factor of 3.

Precision measurement of shape and position tolerance plays an important role and significance in manufacturing industry. It is an important link to measure and guarantee the quality of manufacturi ng. Especially for large-scale precision parts, the repeated use of measuring tools easily leads to measurement errors. Aiming at the problems of low detection efficiency, complex process and high cost of high precision three-coordinate measuring instrument for large-size parts, the characteristics of contact measurement and non-contact measurement for large-size parts are studied based on the characteristics of large-size parts. A measurement method combining laser ranging with reflective target is proposed, and a rotating shaft for fixing laser launcher is designed. A complete spherical coordinate measuring system is constructed, which is applied to the measurement of straightness, flatness, parallelism, verticality and height difference of large-scale precision machined parts. The corresponding measurement results are obtained in a constant greenhouse. On this basis, under the same temperature conditions, the same shape and position tolerance dimensions of the same part are measured by a three-coordinate measuring instrument. Comparing the results of measurement, it can be seen that the measurement results obtained by the two methods are the same in the range of 0.001 mm, and the measurement efficiency and cost of the laser ranging method have obvious advantages. This paper also gives the method of measuring the shape and position tolerance of large-scale precision parts.

The new application Geometrical Tolerancing developed for usage during lectures at technical universities as well as for the enhancement of vocational trainings for design, manufacturing and metrology engineers working in industry is presented. The application capabilities are shown and discussed on base of the selected screen shoots. The suggestive 3-D animations and multicolour drawings with intuitive user interface are employed to effectively familiarize the application user with definitions of form, orientation, location and run out tolerances. The tolerance zones for toleranced integral or derived features are clearly visualized and then shrunk to show particular deviations. The role of the datums and datum systems for establishing involved tolerance zones is explained in details. The restrictions for the part geometry imposed by specified maximum material requirement or least material requirement that combine requirements for size of the features of size and the geometrical tolerance to one aggregated functional requirement are shown. The concepts of the geometrical deviations evaluation by coordinate measuring techniques or workpiece verification by hard gauges are demonstrated for the selected tolerances with case studies.

The Precision Micro-Assembly Machine was developed to manufacture the ICF targets, which have submillimeter-sized components with micrometer sized features. The machine provides simultaneous manipulation of three objects in a 3-cm3 operating arena and can stitch together multiple millimeter-scales operating arenas over distances spanning tens of centimeters with micrometer-level accuracy. In this report, we will discuss the technologies that are merged to help assist the research community with micro-component fabrication. Furthermore, we also present the design of the online monitoring system, which contains two kinds of non-contact measurement system, microscopic image and laser confocal. The online monitoring system can characterize the positions of the target components during the assembly process. The effect and mathematic model of on-line measuring was analyzed. The results of target assembly experiments show position tolerance of the assembly is not more than 10μm.

This paper presents a method for tolerance balancing in machining process planning. The surface position tolerance (SPT) method offers several advantages in comparison with the tolerance charting technique. These advantages arise from the separate consideration of the datum and machining surface position capabilities. To solve the problem of tolerance balancing, the mathematical model used in the literature is adapted to the SPT method. When solving the problem, the objective of maximizing process tolerances was chosen. The proposal was applied to a problem that has been used by many authors in the literature and so a wide comparison can be made of the results. The solution enables the tolerances in the process to be improved and the solution can also be optimized with respect to the capability of the fixture.

For water depths greater than 60m floating wind turbines will become the most economical option for generating offshore wind energy. Tension mooring stabilised units are one type of platform being considered by the offshore wind energy industry. The complex mooring arrangement used by this type of platform means that the dynamics are greatly effected by offsets in the positioning of the anchors. This paper examines the issue of tendon anchor position tolerances. The dynamic effects of three positional tolerances are analysed in survival state using the time domain FASTLink. The severe impact of worst case anchor positional offsets on platform and turbine survivability is shown. The worst anchor misposition combinations are highlighted and should be strongly avoided. Novel methods to mitigate this issue are presented. Science Foundation Ireland Centre MaREI - Centre for Marine and Renewable Energy

International audience; Maximum and least material requirements describe the strictly necessary fittability and accuracy functional requirements for an assembly involving connections with clearances. In the ISO 2692:2014 [1] dimensioning and tolerancing standard, the writing of this requirement violates the principle of independency and is limited to features of size. This paper proposes two complementary writings and several explanations for the application of the concepts. In order to make the definitions consistent with those of ISO 1101:2012 [2] standard, the requirements are defined by means of unilateral tolerance zones. For features of size, the dimension of the tolerance zone for the specified surface and for the reference is written directly between brackets in the specification. For all complex surfaces, the tolerance zone is defined by an offset surface of the nominal surface. The offset value is written between braces. The definitions of form, location and orientation specifications with these modifiers are given for simple elements and for a pattern of holes. Composite specifications, which associate orientation and location tolerance zones with respect to the same nominal, are defined. An example with flutter on a primary reference shows that it is no longer possible to use all the degrees of freedom to associate the subsequent references. The use of an orientation plane to deal with unidirectional chains of dimensions is defined. In terms of metrology, the characteristic to evaluate is the margin between the actual surface and the limit surface of the tolerance zone when the tolerance zone on the references is respected. This margin enables one, for example, to determine a capability. Three applications present an assembly of a mechanism with clearances, a connection with a complex surface and a 3D chain of dimensions at least material which requires a composite specification.

We proposed micro lens array coupling for multi-layered optical printed board. Optical coupling efficiency and optical positional tolerance of micro lens are discussed by ray trace simulation CAD. Polymer micro lens arrays can be fabricated easily by using UV curable resin. Our preliminary simulation indicated that four layers pitch of 125μm of optical printed wiring board is feasible for high coupling efficiency and high optical positional tolerance.

PurposeThe purpose of this paper is to investigate the process of jamming of the hollow parts on the shaft and to derive a mathematical model for jamming in an assembly process.Design/methodology/approachThe mathematical model for jamming of parts on the shaft in an assembly process is based on the sizes, geometry, angular declination of part and shaft axes, and the frictional factor.FindingsThe equation for angular positional tolerance of coaxial parts and shafts, based on their geometry and sizes and leading to jamming, was derived.Research limitations/implicationsA mathematical model of parts jamming on the shaft is developed for assembly mechanisms. This research does not consider flexible deformations of components in assembly mechanisms, which results in the axis concentricity of part and shaft in the assembly process.Practical implicationsThe results presented in the form of angular positional tolerance for coaxial parts and shafts based on their geometry and sizes make it possible to avoid the jamming of the parts. The results allow for formulating the angular positional tolerance of the assembly mechanisms that clamp the parts.Originality/valueThe proposed method for calculating the angular positional tolerance of coaxial parts and shafts for the assembly process should allow for increasing the reliability of the assembly process in the manufacturing industry.

Many applications in industrial robotics such as applying adhesives or cutting require movements of the tool in the process relevant speed. The path in space is programmed by the user as sequence of Point-to-point motion commands, linear and circular motion commands. But in general the tool has to stop in the transition between two path segments. If the programmer use spline or fly by commands, it is possible to move through a via point or close to that point without a stop. But by specifying the appropriate parameters that affect the spline or fly by method the user can not directly influence the deviation from the desired speed and the deviation from a via point. Here a user-friendly solution for the transition between line segments is presented. The tool CorDe (Corner Drive with Defined Speed) visualizes the characteristic of the distance to the corner (position tolerance) depending on the speed deviation. The user can choose an adequate pair of distance and speed deviation. The tool can be used to calculate the time series of the poses. It is also possible to set up a code generator which generates commands in the available robot programming language to approximate the motion generated by CorDe. CorDe has been tested in simulations and experiments.

International audience; This paper depicts a new CAT (Computer Aided Tolerancing) system called Quick GPS (Geometrical Product Specification), for assisting the designer when specifying the functional tolerances of a single part included in a mechanism, without any required complex function analysis. The mechanism assembly is first described through positioning table formalism. In order to create datum reference frames and to respect assembly requirements, an ISO-based 3D tolerancing scheme is then proposed thanks to a set of rules based on geometric patterns and TTRS (Technologically and Topologically Related Surfaces). Since it remains impossible to determine tolerance chains automatically, the designer must impose links between the frames. The CAT system we developed here proposes ISO based tolerance specifications to help ensure compliance with the designer's intentions saving on time and eliminating errors. This paper will detail both the set of tolerancing rules and the designer's approach. The Quick GPS system has been developed in a CATIA V5 environment using CATIA VBA and CATIA CAA procedures.

SummaryWe easily recognize objects and faces across a myriad of retinal images produced by each object. One hypothesis is that this tolerance (a.k.a. “invariance”) is learned by relying on the fact that object identities are temporally stable. While we previously found neuronal evidence supporting this idea at the top of the nonhuman primate ventral visual stream (inferior temporal cortex, or IT), we here test if this is a general tolerance learning mechanism. First, we found that the same type of unsupervised experience that reshaped IT position tolerance also predictably reshaped IT size tolerance, and the magnitude of reshaping was quantitatively similar. Second, this tolerance reshaping can be induced under naturally occurring dynamic visual experience, even without eye movements. Third, unsupervised temporal contiguous experience can build new neuronal tolerance. These results suggest that the ventral visual stream uses a general unsupervised tolerance learning algorithm to build its invariant object representation.

Our previously reported method of accurately simulating the performance of a quadrupole mass filter (QMF) has been applied to the investigation of the effects of electrode positional tolerance on the performance of a QMF when operated in stability zone 3 (a ≈ 3.16 and q ≈ 3.23). Simulations for single- and dual-electrode positional errors have been undertaken. Single-axis errors produced changes in mass peak shape that are similar to those previously reported for zone 1. Compound errors produce changes in mass peak shape that are approximately a summation of the effects obtained from individual single-axis errors. Our results show that the direction of the electrode displacement, not the electrode, is the important factor in determining the effect on QMF performance. We also show that the effects of an individual electrode radius tolerance result in changes to the mass peak shape that are similar to those produced by individual electrode positional errors. Simulations also show the suitability of unbalanced excitation voltages as a method of compensating for mechanical tolerance when operating in zone 3. From these results, we are able to provide suitable limits for the voltage accuracy and stability when employing this method of compensation.

A literature review of sheet metal forming errors as well as geometrical dimensions and tolerances (GD&T) shows that the theoretical means for the allocation of process tolerances with respect to GD&T are insufficient. In order to judge the influence of geometrical process errors (e.g., angular errors of bends), two typical sheet metal designs with parallelism and a position tolerance are studied. These case studies comprise a detailed analysis of tolerance chains including angular errors of bends and their positions. The resulting errors are compared with those resulting from length dimensional process errors and conclusions are drawn.

The present paper addresses the assignment of geometrical position tolerances in reverse engineering. Specification of manufacturing position tolerances for a reconstructed component of an existing mechanical assembly constitutes a complicated task that requires a well-grounded approach. Among features of size, cylindrical features such as holes in conjunction with pegs, pins, or screws are the most frequently used for critical functions, as are the alignment of mating surfaces or the fastening of mating parts. The relationship between mating features is classified either as a fixed or as a floating fastener type. The presented method focuses on the fixed fastener case. It is based on the systematic formulation of dimensional and geometrical relationships and constrains that allow for rational computer-aided processing and evaluation of the measured data from the reference parts, for which appropriately developed algorithmic tools are used. It is shown that the method is reliable, provides for realistic results, and is also time and cost competent as compared with the conventional trial-and-error methods. A case study demonstrates the concept and method.

Geometric and dimensional tolerances must be determined not only to ensure proper achievement of design function but also for manufacturability and assemblability of mechanical assemblies. We are investigating the degree to which it is possible to automate tolerance assignment on mechanical assemblies received only as STEP AP 203 (nominal) geometry files. In a previous paper, we reported on the preprocessing steps required: assembly feature recognition, pattern recognition, and extraction of both constraints and directions of control (DoC) for assembly. In this paper, we discuss first-order tolerance schema development, based purely on assemblability conditions. This includes selecting features to be toleranced, tolerance types, datums, and datum reference frames (DRFs), and tolerance value allocation. The approach described here is a combination of geometric analysis and heuristics. The assumption is that this initial geometric dimensioning and tolerancing (GD&T) specification will be sent to a stack analysis module and iterated upon until satisfactory results, such as desired acceptance rates, are reached. The paper also touches upon issues related to second-order schema development, one that takes intended design function into account.

All technological advancements come about by exploration of ideas through research. Fermi National Accelerator Lab is actively participating by conducting the high energy particle physics experiment ``Muons to Electrons" (Mu2e). In this experiment, scientists within the Mu2e collaboration will try to understand the relationship between two particles, the Muon and its subsequent conversion into the lighter mass electron without any additional neutrinos. To do this, a high intensity muon beam will be generated and then transported to the Detection Solenoid (DS). The Muon Beam Stop (MBS) is the last component within the bore of the detection solenoid. The MBS will be assembled onto a rail system within the DS bore. Additional structures capable of effectively transporting and supporting the MBS weight during installation, alignment and testing are necessary. The structures will need to accurately position the components to meet the experiment’s general tolerance of $\pm$2mm. The designed structures must effectively hold up the MBS for the life of the experiment and absorb deflections from the ground during the installation. To effectively transport and support the MBS, two separate joint structures were designed for each end of the MBS and each will ride on two separate surfaces. The leading-end into the DS Bore has a large spherical joint capable of rotation in all directions while the back end allows for rotation as a result of floor deflections. The structures have both been analyzed using ANSYS and they satisfy safety requirements with a safety factor larger than 4.0 while adhering to the positional tolerance of $\pm$2mm. Design drawings have been prepared and have also been approved for fabrication by the Beamline engineering group of the Mu2e Experiment.

Surgical robots are usually controlled by the method of the independent PD or the PD model based on gravity compensation. However, the system is still a open loop control with both of the control models. The two models can not consider the dynamics effectively either. The position error can not be guaranteed. To solve the problem, a torque control model based on dynamic model and adaptive model is proposed. And the position tolerance of PD control based on gravity compensation and that of control based on Torque Control stability theory are compared by Matlab software. The maximal tolerance of the new method is red robot end-effector is 0.15mm.

A frequently used geometrical tolerance is the position tolerance. When it is assigned at the maximum material condition (MMC), an increase in the position tolerance is allowed, equal to the departure of the particular feature from the maximum material condition size. Neither concept - position tolerance and maximum material condition - analytically related with the exact coordinate dimensions that locate the feature. A feature position is usually allocated on the basis of its theoretically exact co-ordinate dimensions, whereas positional accuracy is pursued through an appropriate planning of the machining process in conjunction with appropriate machine tool(s) and/or jig(s). Exploitation of the MMC tolerance bonus is taken into account mainly during part inspection in order to reduce rejects. Such an approach is not systematic, considering that the MMC benefits are not taken directly into account in the process planning stage in order to control the overall process cost. In this paper, the permitted manufacturing errors of a feature size and position are considered and studied simultaneously in an analytical way. It is shown that a lower process capability (PC) requirement can then be established that leads to a significant process cost reduction. An application example demonstrates the use of the method and the obtained results are discussed.

Appropriate and cost effective assignment and interpretation of dimensional and geometrical tolerances, in conjunction with tolerancing principles such as the maximum material condition (MMC), constitute a major area of concern for manufacturing SMEs. This is particularly true for the process planning stage, where production operations and parameter values establish the final product quality and cost. A frequently used geometrical tolerance is the position tolerance. It allows at least 57% more space for feature allocation without affecting product quality and is very useful for accurate specification of multiple-hole assemblies. Feature allocation becomes further relaxed in case a position tolerance is assigned to the MMC. This assignment is mainly exploited during inspection, because it permits fewer rejections. In terms of cost, it is advantageous to systematically integrate the MMC tolerance bonus into the position tolerance at the process planning stage. A methodology that allows a new MMC-adapted po...

Tolerances impose restrictions on the possible deviations of features from their nominal sizes/shapes. These variations of size/shape could be thought of as deviations of a set of generalized coordinates defined at some convenient point on a feature. Any tolerance specification for a feature imposes some kind of restrictions or constraints on its deviation parameters. These constraints, in general, define a bounded region in the deviation space. In this paper, a method has been presented for converting tolerance specifications as per maximum material condition (MMC)/least material condition (LMC)/regardless of feature size (RFS) material conditions for standard mating features (planar, cylindrical, and spherical) into a set of inequalities in a deviation space. Both virtual condition boundaries Virtual condition boundary: A constant boundary generated by the collective effects of a size feature's specified MMC or LMC material condition and the geometric tolerance for that material condition. (VCB) and tolerance zones are utilized for these mappings. The mapping procedures have been illustrated with an example. Note to Practitioners-This paper deals with methods to convert tolerance specification as per ASME Y14.5M into a set of generalized deviation of features and vice-versa. These are intermediate relationships that are required for use in deviation-based tolerance synthesis methods. In this work, different examples have been presented to show how different tolerance specifications (such as positional tolerance at maximum material condition (MMC), least material condition (LMC), etc.) applied to different features could be treated on a generalized basis for tolerancing of manufactured parts.

The functional tolerancing process for complex mechanisms needs the study of the behavior of mechanical joints. The use of the Computer-Aided Design system helps in carrying out this task. This paper presents an effective new approach for decomposing a global geometric functional requirement of the mechanism into geometric specifications defined on key components (parts and sub-assemblies). A recursive tolerancing method serves to identify and functionally specify the key components related to a tolerance-chain. A geometric variation model, based on the invariant degrees of freedom (DOFs) of the datum reference frames and tolerance zones, enables validating a datum reference system built on the positioning features of a component and then deducing the influential mechanical joints. Formalized simple rules based on the topology of parts have also been developed for validating a datum reference system. A geometric specification defined on a sub-assembly has been introduced as a new geometric functional requirement: this provides the designer with an effective recursive tool for ensuring the functional tolerancing of the entire assembly. The proposed approach is straightforward to implement and has been devised from the concept of standardized specifications, with the particularity that it is capable of treating cases in which the positioning features are not perpendicular.

The use of datum targets within Geometric Dimensioning and Tolerancing (GD&T) is commonplace in industry today. Datum targets are used primarily for manufacturing and inspection setups where it is not practical to have tooling that contacts the entire surface of the datum. Establishing a simulated datum from datum targets may be done physically or mathematically. In the process of establishing a simulated datum, there are several possible sources of variation. Any variation or error in establishing the datum will manifest itself as variation or error in the measurement of the distance between the feature and the datum. This paper examines the effect of variation in datum targets on part acceptance using both mathematical analysis and simulation. The focus of this examination is diametric positional tolerance of holes that reference the datum established by datum targets. A three-dimensional mathematical model of the hole position error with respect to the datum target variation is developed. Then, simulation is adopted to identify the major sources of hole position error due to errors in datum targets. It is found that the datum target variation has a profound effect on the measured location of holes referencing those datums. Explanation and validation for accepted practice are offered and some additional basic guidelines are developed for the placement of datum targets relative to hole patterns.

We propose a precise submicrometer alignment technique for lenses employing high-power laser irradiation. We investigate the mechanism in detail, and show that manipulation of the lenses is achieved in all directions, for the tightest positional tolerance. In particular, our proposed technique enables lens alignment by irradiating only the top of the lens holder making it suitable for high-density integrated multi-channel systems. With this technique, we have successfully developed the first lens-coupled hybrid integrated optical system for a 100 Gbit/s Ethernet transmitter optical sub-assembly.

In planetary transmissions, the input torque is split between a number of parallel sun-pinion-ring gear paths. Under ideal conditions, each parallel path carries the same amount of torque. However, manufacturing errors in the pinion pin-hole location cause unequal load sharing between the parallel paths. The nature of this load sharing behavior depends upon the number of pinions in the planetary system. This load sharing behavior is studied for 4, 5 and 6 pinion variants of a planetary transmission. Critical manufacturing tolerances are identified and loss function curves are generated. The effects of sun gear support stiffness, pinion needle bearing stiffness, and input torque on the load sharing results are also studied. It is shown that as the number of pinions in a planetary transmission increases, the pin-hole position error tolerance has to be tightened in order to reap the full benefits of load sharing between the pinions. Gear System Analysis Modules (GSAM) is an analytical tool that can model entire gear systems and will be used in this paper to quantify the load sharing between pinions. The numerical techniques implemented in GSAM will be briefly reviewed.Copyright © 2003 by ASME

A new mathematical model for representing geometric tolerances is applied to polygonal faces and is extended to show its sensitivity to the precedence (ordering) of datum reference frames. The model is compatible with the ASME/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map® 2 , a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, position, form, and orientation. Every Tolerance-Map is a convex set. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used to allocate size and orientational tolerances; the same relations also can be used to identify sensitivities for these tolerances. All stackup relations can be met for 100% interchangeability or for a specified probability. Methods are introduced whereby designers can identify trade-offs and optimize the allocation of tolerances. Examples are presented that illustrate important features of the new model.

Circular, cylindrical, or spherical features are fundamental geometric features in engineering. As precision requirement becomes more stringent, it is not sufficient to consider only size tolerance of circular and cylindrical parts. However, currently there is no quantitative and systematic way of assigning circularity and cylindricity tolerances. This paper investigates how to specify circularity tolerance quantitatively for 2D assemblies. Statistical matrices to quantify positioning error of two perfectly circular mating parts subject to size tolerance for both clearance and transition fit conditions are first developed. The analysis is then extended to nonideal profiles whose profile errors are assumed to deviate from a best-fit circle according to a normal distribution. The assumption of the normal distribution is then removed for more general results via computer simulation. For this purpose, an experimentally verified profile model is used to generate realistic profiles as those produced by various machining processes. Numerous pairs of these realistic profiles are then assembled virtually using Monte Carlo simulation to quantify their positioning errors. The simulation results and the analytical results are compared for cross-checking. Finally, systematic design procedures are proposed to assign circularity tolerance by prescribing a fit condition with a desirable process capability. By the nature of circularity tolerance, this paper addresses a 2D assembly. The result of this 2D analysis can be a foundation for more complicated 3D problems, such as assigning cylindricity tolerance.

The quality of a set of manufactured features with complex geometric dimensioning and tolerancing call-outs is discussed. Since measurements taken during the inspection of these manufactured features do not always conform to the usual normality assumpti..

Conformance to a specified part geometry is key to achieve product quality. Geometric tolerance control on Coordinate Measuring Machines is a critical issue as parsimony in the set of probed points dictated by economic considerations conflicts with the requirement of full field inspection mandated by tolerance standards. Evaluation of uncertainty originated by sampling errors takes therefore a high priority level. The case of position tolerance control on a hole axis and related uncertainty analysis is examined in the paper via Monte Carlo simulation. Results exhibit a remarkable uncertainty related to a number of steps involved in the control method. A comprehensive statistical analysis is shown to be required if risk of failure to reach the correct decision in assessing part conformance is to be kept under control.

The technical difficulty of balancing large data capacity with a high data transfer rate in holographic data storage systems (HDSSs) is significantly high because of tight tolerances for physical perturbation. From a system margin perspective in terabyte-class HDSSs, the positioning error of a holographic disc should be within about 10 µm to ensure high readout quality. Furthermore, fine control of the positioning should be accomplished within a time frame of about 10 ms for a high data transfer rate of the Gbps class, while a conventional method based on servo control of spindle or sled motors can rarely satisfy the requirement. In this study, a new compensation method for the effect of positioning error, which precisely controls the positioning of a Nyquist aperture instead of a holographic disc, has been developed. The method relaxes the markedly low positional tolerance of a holographic disc. Moreover, owing to the markedly light weight of the aperture, positioning control within the required time frame becomes feasible.

The purpose of this paper is to improve the features of Health Screening Test System (HSTS) on Social Security Organization (SOCSO) program as physical evaluation for musculoskeletal disable workers (MSDs). SOCSO existing functional testing system are not suitable because of the evaluation was recorded manually peg board too high for Asian people. The occupational therapist whose involve in all the procedures is just doing the judgment in times to determine the capability of the patients. The functional capacity evaluation (FCE) technique is based on the functional range of motion evaluation that consist of positional tolerance respecting to time-motion testing on HSTS peg board and it is by referring to the original work movement. The main features of HSTS are able to measure speed, acceleration and evaluation of SOCSO’s patients for returning to work based on SOCSO’s requirement. In order to validate the accuracy of the proposed model, HSTS is used to evaluate the patient’s positional tolerance and then the result would be compare over the time frame which is Method Time Measurement (MTM) standard. This method is able to provide information and feedback for therapies as a status of patients. It is found that the proposed model is superior in getting the accurate time test for patient’s movements besides practicable and suitable for physical evaluation on MSD patients.

The manual, synchromesh transmission synchronizer design factors that are essential in its sizing and selecting have been addressed. Derivations, mathematical algorithms, and dimensioning and tolerancing schemes have been worked out to assist in this endeavor. Attempt is made to show that the design and calculations of physical parameters must go hand in hand. That the calculations of synchronizer physical parameters should be supported by scrupulously dimensioning and tolerancing the components design to achieve the intended functional objective. A mathematical algorithm is developed that facilitates establishing the sleeve and blocker ring chamfer angle relationship with the synchronizer size, coefficient of friction, cone torque, and index torque. The relationship is presented graphically in a unique manner identifying the clash and hard shift zones. As such, it allows sizing the synchronizer and selection of the parameters for a given application for comfortable shiftability between the two extremes of clash and hard shift. The synchronization torque requirement for a given synchronization time with known gear ratios and steps has been calculated. Total energy dissipation and rate of energy dissipation method has been derived. The synchronization episode is dissected into six distinct events that are used illustratively for iteratively dimensioning and tolerancing of the synchronizer components. The components that play significant role in each event are identified and related to a specific physical parameter. Performance failure conditions such as clash, double bump, scratchiness, and harshness are also defined from the design and manufacturing point of view. Keywords: synchronizer design: mathematical analysis using free body diagrams; tolerancing the components individually and together; failure modes and affects due to flawed analysis; dimensioning; tolerancing; manufacturing

We present an optical chip-to-chip coupling scheme with large misalignment tolerances. The coupling system is based on a multi-material platform with a polymer waveguide for the interconnection between chips. Simulation shows a position tolerance (3 dB coupling efficiency) of up to 1.0 µm when the polymer waveguide diameter equals 6.0 µm. The polymer waveguide can be easily fabricated by using a 3D laser lithography technique. Article not available.

Form tolerance plays an important role in representing features on a solid model. Reported research works on tolerance indicate that the current focus is on modeling form variations directly without defining the form tolerance zones. This paper presents a mathematical definition of the flatness tolerance zone using various parameters to describe its characteristics. By calculating the limits of these parameters, the size, location and orientation of the tolerance zone can be determined. Combining the flatness and size tolerance zones, a final zone can be obtained. This zone represents the actual region of space within which the toleranced surface must lie in order to satisfy both the size and form tolerances. The developed mathematical model is implemented in a 3-D modeling environment so that the user can specify tolerance types and values, and model the tolerance zones. This can be used in verifying the interference between parts during assembly modeling.

Position tolerance is a three dimensional geometric specification used to control the location of features of size with respect to a set of datum features or with respect to each other. Among features of size, hole is perhaps most frequently encountered in the production of industrial parts. To control the relationship between a set of holes, feature relating position tolerance (referred to as FRTZ) is used. FRTZ is applied to ensure proper assembly between mating parts. Assessment of feature relating positional error is a difficult task due to the absence of a datum reference frame whose function is to impose translational and rotational constraints on the part. Existing techniques for the assessment of FRTZ are either too expensive, or time consuming and inaccurate. This paper presents a mathematical model of three-dimensional feature-relating positional error and proposes a sound methodology for its evaluation. The results of performance analysis indicate that the proposed methodology is robust, accurate and efficient. The procedure has been implemented in a computer-aided inspection system.

A 180° light path conversion device with a tapered self-written waveguide (SWW) is proposed for optical interconnection. Larger tolerance width and improved light-coupling efficiency are expected when coupling this device to optical devices, because the size of the end faces at both the light-emitting and light-receiving devices can be optimized, owing to the tapered shape of the SWW. A ray-tracing simulation indicates that positional tolerance width of 1 dB down can be increased more than two fold by fabricating a tapered core. We constructed a prototype device with a tapered SWW and achieved optical coupling efficiency of -3.6 dB.

A general geometric framework is developed to quantify the structure of positional tolerance evaluation. The data graph, overlay graph, and configuration framework of a feature set is defined and used in the evaluation of positional tolerance. Two functionals based on the configuration framework are introduced and lead to the development of optimal matings. The configuration functional quantifies the amount of “turning” the framework will allow while satisfying the mating condition, while the mating functional is used to assess optimal mating conditions. A constructive geometric procedure is used to develop the configuration and mating functionals for a given feature vector and tolerance specifications. Numerical examples are used to illustrate the form of the functionals and the procedures involved in the analysis.

The composite positional tolerance evaluation problem for planar point features and circular tolerance zones is defined and characterized under necessary and sufficient conditions. This model is then generalized to the circular feature case, and the solution to the circular feature–circular tolerance zone problem is characterized analogous to the point feature model. The circular feature–circular tolerance zone problem is formulated as a containment model and solved as a constrained nonlinear program. The three-dimensional spherical containment model is also formulated and numerical examples are used to illustrate the methodology in the two- and three-dimensional cases.

Joint clearance in mechanisms and robots leads to uncertainty in function deviation. Unlike the effect of the link tolerance on the performance quality, the uncertainty effect of the joint clearance to the performance can not be eliminated by calibration because of the random nature. In this paper, based on the probability theory, a general probability density function (p.d.f.) of the endpoint of planar robots is established. The p.d.f. of the endpoint of a planer robot is equivalent to that of endpoint of a string of planar joint deviation vectors. By grouping the planar joint deviation vectors and establishing the structural constraint conditions between the vector groups, a basic approach of deriving the general p.d.f. of spatial robots is also presented. Based on the general p.d.f. of the endpoint, the distribution functions of the robot endpoint for any position tolerance zone and any joint distribution type, can be derived. The method is demonstrated by using some common types of position tolerance zones with uniform as well as normal distribution for joint clearance. The distribution functions of the robot endpoint are calculated and tabulated. These distribution functions and tables provide a convenient way to obtain the probability value for a robot to position its end point within a desired tolerance zone, and to determine the joint clearance value for the desired type of tolerance zone and the prescribed probability value of position repeatability.

This paper presents a new approach to optimum tolerancing of components in an assembly such that all interaction requirements are met. The requirements may be for unilateral tolerance for control of clearance and interference or they may be for bilateral tolerance control. A model showing the relationship between components is constructed directly from the design. Using the model, coupled with a unique algorithm, a set of linear equations is formulated based on the design constraints and assembly requirements. The linear equations are then solved to determine the optimum tolerances of the assembly.

Geometric dimensioning and tolerancing (GDT) has been playing an important role in specifying the geometry of part features during the product design stage. Tolerance stack analysis is then used to study the conformity of the parts to the tolerance zone. Performing stack analysis is time consuming because geometric tolerances are complex to compute. This paper presents a technique to formulate the bonus and shift tolerances (due to positional callout) and convert them to equal bilateral expressions as in a coordinate tolerance system. An example is used to demonstrate the effectiveness of the expressions. The usage of the expressions is less conceptual and this makes the application simple and direct. Most importantly, the results are shown to be accurate and reliable.

This article presents a computational scheme for representing and interpreting the geometric tolerances (mainly size, orientation and position tolerances) assigned to polyhedral objects. The proposed representational scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface's model variables. Those model variables are constrained by relations derived from tolerance zones. This article addresses two questions: (i) how to describe the tolerance zones according to different tolerance specifications? and (ii) how to vary the model variables when the variational models (of the part) are instantiated? The scheme has been fully implemented in an object-oriented programming environment.