Research in modularization of product families reveals numerous individual cause and effect impacts of modularity on a firm. There are clearly many interrelated positive and negative economic impacts arising from different activities of the firm impacted by the modular product structures. This makes the construction of an economic business case for modularity difficult, where often the benefits are reduced indirect costs. This paper presents a literature-based network model of how modular product structures affect firm’s economics across the design-to-manufacturing life cycle phases. It shows how (1) changes on modularity properties may lead to (2) different effects within the product’s life cycle phases that (3) have an economic impact on the firm. For instance, modularization can prolong development time of a platform, while shortening the subsequent development times of product variants and lowering manufacturing costs. To validate the proposed model, the given effect chains were compared by industrial experts against nine case study modularization projects by marking effects that were experienced and observed in their projects. The results first revealed that in design, an increase of commonality drove component reuse leading to lower development costs per unit. Second, in procurement, it was found that increased modularity caused better predictability, less purchasing orders, and better purchasing conditions that ultimately lead to lower costs. Third, in production, it was found that a smaller variety of components allowed less process variety, leading to fewer and more optimized processes and therefore lower production costs. We present these cause and effect impacts of modularity as drivers for quantifying the economic impact of modularity.

Isomorphism (structural similarity) of kinematic chains (KCs) of mechanisms is an important issue in the structural synthesis, which must be identified to avoid the duplicate structures. Duplication causes incorrect family size, i.e., distinct KCs with a given number of links (n) and degree of freedom (dof). Besides simple joints kinematic chains (SJKCs), multiple joints kinematic chains (MJKCs) are also widely used because of their compact size and the methods dealing with such KCs are few. The proposed method deals with two different structural invariants, i.e., primary structural invariants (provide only the necessary condition of isomorphism), such as link connectivity number (LCN) of all the links, link connectivity number of chain (CCN), joint connectivity number (JCN) of all the joints, and joint connectivity number of chain (JCNC), and secondary structural invariants (provide the sufficient condition of isomorphism), such as power transmission (P) and transmission efficiency (T e ). Primary structural invariants are calculated using a new link–link connectivity matrix (LLCM), whereas secondary structural invariants are calculated using the concept of entropy of information theory. The method has been successfully tested for 10 and 11 links MJKCs (illustrative examples taken in the paper) and for the families of 18 MJKCs with 8 links, 2 MJs, 1-dof, and 3 independent loops; 22 MJKCs with 8 links, 1 MJ, 1-dof, and 3 independent loops; and 83 MJKCs with 9 links, 1 MJ, 2-dof, and 3 independent loops.

Ocean wave power is a promising renewable energy source. It has, however, been difficult to find a cost-effective solution to convert wave energy into electricity. The harsh marine environment and the fact that wave power is delivered with large forces at low speed make design of durable mechanical structures and efficient energy conversion challenging. The dimensioning forces strongly depend on the wave power concept, the wave energy converter (WEC) implementation, and the actual power take-off (PTO) system. A WEC with a winch as a power take-off system, i.e., a winch-based point absorber (WBPA), could potentially enable a low levelized cost of energy (LCOE) if a low-cost, durable and efficient winch that can deal with peak loads can be developed. A key challenge for realizing such a winch is to find a force transmitting solution that can deal with these peak loads and that can handle up to 80 million cycles during its life. In this article, we propose a design solution for a force transmitting chain with elastomer bearings connecting the links of the chain. With this solution no sliding is present, and the angular motion is realized as elastic shear deformations in the elastomer bearings when the chain is wound onto the winch drum. The elastomer bearings were designed for low shear stiffness and high compression stiffness, and the links were designed primarily to minimize the number of joints in the chain. Thereby, the maximum allowed relative angle between the links when rolled up over the drum should be as large as possible within practical limits. Finite element-based topological optimization was performed with the aim to increase the link strength to weight ratio. A test rig for a first proof of concept testing has been developed, and preliminary test results indicate that this chain concept with elastomer bearings can be a potential solution for a durable chain and should be analyzed and tested further for fatigue and sea operations.

The structural synthesis of Baranov trusses is still an open problem, although Baranov trusses are widely used in the design and analysis of mechanisms and robots. This paper proposes a systematic method for the structural synthesis of Baranov trusses. First, the definition review and the graph-form representations of Baranov trusses are proposed. Second, seven propositions on structural characteristics of Baranov trusses are concluded. Then, based on the set of constraint equations and a rigid subchain detection algorithm, a systematic method is presented to synthesize the complete set of Baranov trusses with a specified number of links. Finally, the synthesis results of contracted graphs (including valid and rigid contracted graphs) and topological graphs of Baranov trusses with up to 13 links are provided, and the synthesis methods and results between ours and the ones in the existing literature are compared and discussed in detail.

A material's design revolution is underway with a focus to design the material microstructure and processing paths to achieve certain performance requirements of products. A host of manufacturing processes are involved in producing a product. The processing carried out in each process influences its final properties. To couple the material processing-structure-property-performance (PSPP) spaces, models of specific manufacturing processes must be enhanced and integrated using multiscale modeling techniques (vertical integration) and then the input and output of the various manufacturing processes must be integrated to facilitate the flow of information from one process to another (horizontal integration). Together vertical and horizontal integration allows for the decision-based design exploration of the manufacturing process chain in an inverse manner to realize the end product. In this paper, we present an inverse method to achieve the integrated design exploration of materials, products, and manufacturing processes through the vertical and horizontal integration of models. The method is supported by the concept exploration framework (CEF) to systematically explore design alternatives and generate satisficing design solutions. The efficacy of the method is illustrated for a hot rod rolling (HRR) and cooling process chain problem by exploring the processing paths and microstructure in an inverse manner to produce a rod with specific mechanical properties. The proposed method and the exploration framework are generic and support the integrated decision-based design exploration of a process chain to realize an end product by tailoring material microstructures and processing paths.

The umbrella linkage is one of the most classical deployable mechanisms. This paper concentrates on topological structural design of a family of umbrella-shaped deployable mechanisms based on new two-layer and two-loop spatial linkage units. First, deployable units are developed systematically from two-layer and two-loop linkage with four revolute pair (4R) coupling chains. Then, mobile connection modes of the deployable units are established based on the conditions of one degree-of-freedom (DOF) and structural symmetry. Finally, umbrella-shaped deployable mechanisms are constructed based on the developed deployable units and the established mobile connection modes. Like umbrellas, the designed deployable mechanisms can be actuated in a simple and reliable way, and those mechanisms have good potential applications in the fields of architecture, manufacturing, space exploration, and recreation.

This paper presents a design methodology and experimental assessment of variable-geometry dies that enable the extrusion of plastic parts with a nonconstant cross section. These shape-changing dies can produce complex plastic components at higher manufacturing speeds and with lower tooling costs than injection molding. Planar, rigid-body, shape-changing mechanism synthesis techniques are used to create the links that comprise the variable-geometry die exit orifice. Mechanical design guidelines for production-worthy dies are proposed. Several dies were designed and constructed to provide significant changes in the cross-sectional shape and area of extruded parts. Experiments were conducted in a production environment. An analysis of the repeatability of the cross-sectional profiles along the length of the part is presented.

Designers often search for new solutions by iteratively adapting a current design. By engaging in this search, designers not only improve solution quality but also begin to learn what operational patterns might improve the solution in future iterations. Previous work in psychology has demonstrated that humans can fluently and adeptly learn short operational sequences that aid problem-solving. This paper explores how designers learn and employ sequences within the realm of engineering design. Specifically, this work analyzes behavioral patterns in two human studies in which participants solved configuration design problems. Behavioral data from the two studies are first analyzed using Markov chains to determine how much representation complexity is necessary to quantify the sequential patterns that designers employ during solving. It is discovered that first-order Markov chains are capable of accurately representing designers' sequences. Next, the ability to learn first-order sequences is implemented in an agent-based modeling framework to assess the performance implications of sequence-learning abilities. These computational studies confirm the assumption that the ability to learn sequences is beneficial to designers.

In machining process planning, it is critical to ensure that the part created following the manufacturing steps complies with the designated design tolerances. However, the challenge is that manufacturing errors are stochastic in nature and are introduced at almost every step of executing a plan, for example, due to inaccuracy of tooling, misalignment of location, etc. Furthermore, these errors accumulate or “stack up” as the machining process progresses to inevitably produce a part that varies from the original design. The resulting variations should be within prescribed design tolerances for the manufactured part to be acceptable. In this work, we present a novel approach for assessing the manufacturing errors by representing variations of nominal features with transformations that are defined in terms of extents of the features' degrees-of-freedom (DOFs) within their design and manufacturing tolerance zones (MTZs). We show how the manufacturing errors stackup can be effectively represented by the composition and intersection of these transformations. Several examples representing scenarios of different complexities are demonstrated to show the applicability of our approach in assessing the influence of manufacturing errors on the design tolerances following a machining plan. Discussions of our approach are provided to address concerns with the accuracy and efficiency as well as to disclose the potential of our approach to enable a tolerance-aware process planning system.

A parallel mechanism possesses several advantages compared to a similar-sized serial mechanism, including the potential for higher accuracy and reduced moving mass, the latter enabling increased load capacity and higher acceleration. One of the most important issues affecting a parallel mechanism is the potential of parallel singularities. Such configurations strongly affect the performance of a parallel mechanism, both in the actual singularity and in its vicinity. For example, both the stiffness of a mechanism and the efficiency of the power transmission to the tool platform are related to the closeness to singular configurations. A mechanism with a mobility larger than the mobility of its tool platform is referred to as a kinematically redundant mechanism. It is well known that introducing kinematic redundancy enables a mechanism to avoid singular configurations. In this paper, three novel kinematically redundant planar parallel mechanisms are proposed. All three mechanisms provide planar translations of the tool platform in two degrees-of-freedom, in addition to infinite rotation of the platform around an axis normal to the plane of the translations. The unique feature of the proposed mechanisms is that, with the appropriate inverse kinematics solutions, all configurations in the entire workspace feature optimal singularity avoidance. It is demonstrated how it is sufficient to employ five actuators to achieve this purpose. In addition, it is shown how including more than five actuators significantly reduces the required actuator motions for identical motions of the tool platform, thereby reducing the cycle times for typical applications.

Robots designed for space applications, deep sea applications, handling of hazardous material and surgery should ideally be able to handle as many potential faults as possible. This paper provides novel indices for fault tolerance analysis of redundantly actuated parallel robots. Such robots have the potential for higher accuracy, improved stiffness, and higher acceleration compared to similar-sized serial robots. The faults considered are free-swinging joint failures (FSJFs), defined as a software or hardware fault, preventing the administration of actuator torque on a joint. However, for a large range of robots, the proposed indices are applicable also to faults corresponding to the disappearance of a kinematic chain, for example, a breakage. Most existing fault tolerance indices provide a ratio between a robot's performance after the fault and the performance before the fault. In contrast, the indices proposed in this paper provide absolute measures of a robot's performance under the worst-case faults. The proposed indices are based on two recently introduced metrics for motion/force transmission analysis of parallel robots. Their main advantage is their applicability to parallel robots with arbitrary degrees-of–freedom (DOF), along with their intuitive geometric interpretation. The feasibility of the proposed indices is demonstrated through application on a redundantly actuated planar parallel mechanism.

Assembly tolerance design for spatial mechanisms is a complex engineering problem that involves a highly nonlinear dimension chain equation and challenges in simplifying the spatial mechanism matrix equation. To address the nonlinearity of the problem and the difficulty of simplifying the dimension chain equation, this paper investigates the use of the Rackwitz–Fiessler (R–F) reliability analysis method and several surrogate model methods, respectively. The tolerance analysis results obtained for a landing gear assembly problem using the R–F method and the surrogate model methods indicate that compared with the extremum method and the probability method, the R–F method allows more accurate and efficient computation of the successful assembly rate, a reasonable tolerance allocation design, and cost reductions of 37% and 16%, respectively. Moreover, the surrogate-model-based computation results show that the support vector machine (SVM) method offers the highest computational accuracy among the three investigated surrogate methods but is more time consuming, whereas the response surface method and the back propagation (BP) neural network method offer relatively low accuracy but higher calculation efficiency. Overall, all of the surrogate model methods provide good computational accuracy while requiring far less time for analysis and computation compared with the simplification of the dimension chain equation or the Monte Carlo method.

Over the last six decades, kinematicians have devised many tests for the identification of isomorphism among kinematic chains (KCs) with revolute pairs. But when it comes to KCs with prismatic pairs, tests are woefully absent and the age-old method of visual inspection is being resorted to even today. This void is all the more conspicuous because sliders are present in all kinds of machinery like quick-return motion mechanism, Davis steering gear, trench hoe, etc. The reason for this unfortunate avoidance is the difficulty in discriminating between sliding and revolute pairs in the link–link adjacency matrix, a popular starting point for many methods. This paper attempts to overcome this obstacle by (i) using joint–joint adjacency, (ii) labeling the revolute pairs first, followed by the sliding pairs, and (iii) observing whether an element of the adjacency matrix belongs to revolute–revolute (RR), revolute–prismatic (RP) (or PR), or prismatic–prismatic (PP) zone, where R and P stand for revolute and prismatic joints, respectively. A procedure similar to hamming number technique is applied on the adjacency matrix but each hamming number is now split into three components, so as to yield the split hamming string (SHS). It is proposed in this paper that the SHS is a reliable and simple test for isomorphism among KCs with prismatic pairs. Using a computer program in python , this method has been applied successfully on a single degree-of-freedom (DOF) simple-jointed planar six-bar chains (up to all possible seven prismatic pairs) and eight-bar KCs (up to all ten prismatic pairs). For six-bar chains, the total number of distinct chains obtained was 94 with 47 each for Watt and Stephenson lineages. For eight-bar chains, the total number is 7167 with the distinct chain count and the corresponding link assortment in parenthesis as 3780(0-4-4), 3037(1-2-5), and 350(2-0-6). Placing all these distinct KCs in a descending order based on SHS can substantially simplify communication during referencing, storing, and retrieving.

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

The remote center of motion (RCM) mechanism is an important component of a minimally invasive surgery (MIS) robot. The feature of the RCM mechanism is that the output link can rotate around a fixed point and translate along an axis which passes the point; however, there is no revolute joint at the fixed point. The 3R1T RCM mechanism, which meets all the degrees-of-freedom (DOF) requirements of arbitrary MIS tools, can be assembled through many methods. An effective method is combining a planar closed-loop 1R1T RCM mechanism and two revolute joints. In this paper, we present an approach to construct 1R1T RCM mechanisms from pantograph mechanisms. First, pantograph mechanisms are divided into seven classifications according to the geometric transformations they represent. The concept of rigid motion tracking mechanism (RMTM) is proposed by combining two equivalent pantograph mechanisms. Then, a novel type synthesis method for 1R1T RCM mechanisms is discussed in detail, and it shows that a 1R1T RCM mechanism can be constructed by assembling an RMTM and a 1R1T mechanism. By this method, several examples are constructed.

This paper presents two integrated planar-spherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crash-lock base. Investigating the crash-lock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar four-bar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planar-spherical overconstrained mechanism with two double-spherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the double-spherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screw-loop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closed-form equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origami-inspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.

The space curve meshing wheel (SCMW) is an innovative gear mechanism based on the space curve meshing theory, and the helix curve meshing wheel (HCMW) is the most common SCMW. In this study, we propose the polyhedral helix curve meshing reducer (HCMR), which is based on the HCMW group. The installation dimension chains of the HCMW pairs are described for different included-angle cases and the HCMW group is produced by combining HCMW pairs. Finally, a polyhedral HCMR is designed with a single input shaft and multiple output shafts, with an adjustable gear box, for which a trial version was produced. The polyhedral HCMR has good application prospects because of its compact structure, high design flexibility, and low cost.

Action origami is a field of origami dealing with models that are folded so that in their final, deployed state they exhibit motion. Hundreds of action origami models exist, many of which use complicated kinematics to achieve motion in their deployed state. A better understanding of the mechanisms used to create motion in action origami could be a foundation for developing a new source of concepts for deployable, movable engineering solutions. This brief presents an approach for evaluating and classifying the mechanisms that enable action origami motion. Approximately 130 action origami models are investigated. Although disguised with artistic elements, it is found that most action origami models are based on a few fundamental mechanisms. A classification scheme is proposed, and an unexplored class of action origami is identified as an area for future origami art.

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis.