Spencer P. Magleby

Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments

The direct linearization method (DLM) for tolerance analysis of 3-D mechanical assemblies is presented. Vector assembly models are used, based on 3-D vector loops which represent the dimensional chains that produce tolerance stackup in an assembly. Tolerance analysis procedures are formulated for both open and closed loop assembly models. The method generalizes assembly variation models to include small kinematic adjustments between mating parts. Open vector loops describe critical assembly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are implicit functions of the resultant assembly dimensions. A general linearization procedure is outlined, by which the variation of assembly parameters may be estimated explicitly by matrix algebra. Solutions to an over-determined system or a system having more equations than unknowns are included. A detailed example is presented to demonstrate the procedures of applying the DLM to a 3-D mechanical assembly.

Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies

Geometric feature variations are the result of variations in the shape, orientation or location of part features as defined in ANSI Y14.5M-1982 tolerance standard. When such feature variations occur on the mating surfaces between components of an assembly, they affect the variation of the completed assembly. The geometric feature variations accumulate statistically and propagate kinematically in a similar manner to the dimensional variations of the components in the assembly.The direct linearization method (DLM) for assembly tolerance analysis provides a means of estimating variations and assembly rejects, caused by the dimensional variations of the components in an assembly. So far no generalized approach has been developed to include all geometric feature variations in a computer-aided tolerance analysis system.This paper introduces a new, generalized approach for including all the geometric feature variations in the tolerance analysis of mechanical assemblies. It focuses on how to characterize geometri...

Accommodating Thickness in Origami-Based Deployable Arrays

The purpose of this work is to create deployment systems with a large ratio of stowed-to-deployed diameter. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in a material with negligible thickness; however, when the application requires the folding of thick, rigid panels, attention must be paid to the effect of material thickness not only on the final folded state, but also during the folding motion (i.e., the panels must not be required to flex to attain the final folded form). The objective is to develop new methods for deployment from a compact folded form to a large circular array (or other final form). This paper describes a mathematical model for modifying the pattern to accommodate material thickness in the context of the design, modeling, and testing of a deployable system inspired by an origami six-sided flasher model. The model is demonstrated in hardware as a 1/20th scale prototype of a deployable solar array for space applications. The resulting prototype has a ratio of stowed-to-deployed diameter of 9.2 (or 1.25 m deployed outer diameter to 0.136 m stowed outer diameter). INTRODUCTION The purpose of this work is to develop deployment systems that unfold from a compact form to a large array. This work ∗Corresponding author: lhowell@byu.edu is motivated by the need for compactly folded solar arrays for space applications. A large ratio of stowed-to-deployed diameter enables large solar arrays to be launched in their compact, folded configuration and then deployed in space to a much larger surface area. For our objectives, a design with synchronous deployment was desired to simplify actuation and deployment. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in paper or other materials with negligible thickness; however, when the application requires the folding of thick, rigid panels, material thickness can inhibit the folding motion. To be rigid-foldable, the panels must not be required to flex to attain the final folded form. This paper describes the approach for modifying the design of an origami six-sided flasher model to accommodate material thickness. This work builds on existing models to present a unique design that is rigid-foldable through two different methods. In the first method, the panels are allowed to flex along their diagonals. In the second method, the panels are affixed to a flexible membrane with discrete gap spacing between the panels. Both folding solutions enable the model to be rigid-foldable.

Dynamic Modeling of Compliant Constant-Force Compression Mechanisms

A mathematical dynamic model is derived for compliant, constant-force compression mechanisms, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force compression mechanism (CFCM) is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully calibrated with empirical data from five separate mechanisms, comprising two basic configurations of CFCMs. The dynamic equation is derived from a generalized pseudo-rigid-body model. This allows every configuration to be represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force mechanism is discovered. There exists a range of input deflection frequencies for which the output force of the mechanism is nearer to constant-force than it is with static input deflections.

Ortho-planar linear-motion springs

Abstract This paper presents an ortho-planar spring design that operates by raising or lowering its platform relative to the base with no rotation. The compact nature of the design, and its non-rotating motion, eliminates the problem of rotation against adjoining surfaces and is less sensitive to variation in assemblies than many current compact springs. Nomenclature is presented to identify different configurations, mathematical equations are provided that accurately model the force–deflection relationships, and a pneumatic valve positioner application is demonstrated.

Compliant Joint Design Principles for High Compressive Load Situations

Buckling failure has been a major obstacle in designing compliant joints in high compression applications. This paper describes two principles, isolation and inversion, that can be successfully applied to many compliant joints to increase their ability to withstand high compressive loads by avoiding buckling-prone loading conditions. Isolation and inversion give rise to a new breed of compliant joints called high compression compliant mechanisms (HCCM). HCCMs have many of the inherent advantages of compliant mechanisms with the additional qualities of high load-bearing joints. This added robustness in compression can be achieved without adversely affecting the kinematic behavior of the joint.

Waterbomb base: a symmetric single-vertex bistable origami mechanism

The origami waterbomb base is a single-vertex bistable origami mechanism that has unique properties which may prove useful in a variety of applications. It also shows promise as a test bed for smart materials and actuation because of its straightforward geometry and multiple phases of motion, ranging from simple to more complex. This study develops a quantitative understanding of the symmetric waterbomb baseʼs kinetic behavior. This is done by completing kinematic and potential energy analyses to understand and predict bistable behavior. A physical prototype is constructed and tested to validate the results of the analyses. Finite element and virtual work analyses based on the prototype are used to explore the locations of the stable equilibrium positions and the force–deflection response. The model results are verified through comparisons to measurements on a physical prototype. The resulting models describe waterbomb base behavior and provide an engineering tool for application development.

A Comprehensive System for Computer-Aided Tolerance Analysis of 2-D and 3-D Mechanical Assemblies

Tolerance analysis of assemblies promotes concurrent engineering by bringing engineering requirements and manufacturing capabilities together in a common model. By further integrating the engineering modeling and analysis with a CAD system, a practical tool for product and process development is created. It provides a quantitative design tool for predicting the effects of manufacturing variation on performance and cost in a computer-based design environment.

Lamina Emergent Mechanisms and Their Basic Elements

Lamina emergent mechanisms (LEMs) are fabricated from planar materials (lamina) and have motion that emerges out of the fabrication plane. LEMs provide an opportunity to create compact, cost-effective devices that are capable of accomplishing sophisticated mechanical tasks. They offer the advantages of planar fabrication, a flat initial state (compactness), and monolithic composition (which provides the advantages associated with compliant mechanisms). These advantages come with the tradeoff of challenging design issues. LEM challenges include large, nonlinear deflections, singularities due to two possible motion configurations as they leave their planar state, and coupling of material properties and geometry in predicting mechanism behavior. This paper defines lamina emergent mechanisms, motivates their study, and proposes a fundamental framework on which to base future LEM design. This includes the fundamental components (created by influencing geometry, material properties, and boundary conditions) and basic mechanisms (including planar four-bars and six-bars, and spherical and spatial mechanisms).

Kinematic Representations of Pop-Up Paper Mechanisms

Pop-up paper mechanisms use techniques very similar to the well-studied paper folding techniques of origami. However, popups differ in both the manner of construction and the target uses, warranting further study. This paper outlines the use of planar and spherical kinematics to model commonly used pop-up paper mechanisms. A survey of common joint types is given, including folds, interlocking slots, bends, pivots, sliders and rotating sliders. Also included is an overview of common onepiece and layered mechanisms, including single-slit, double-slit, V-fold, tent, tube strap and arch mechanisms. Each mechanism or joint is described using a kinematic or compliant mechanism representation. In addition, it is shown that more complex mechanisms may be created by combining simple mechanisms in various ways. The principles presented are applied to the creation of new pop-up joints and mechanisms. The new mechanisms employ both spherical and spatial kinematic chains. Various other applications are also mentioned which could benefit from the use of pop-up mechanism principles. Possible applications include deployable structures, packaging and instruments for minimally invasive surgery.Copyright