John A. Mirth

Circuit Rectification for Four Precision Position Synthesis of Stephenson Six-Bar Linkages

Circuit rectification ensures that a linkage may reach all precision positions without disassembly. Circuit rectification is crucial to the practical synthesis of Stephenson linkages, which have up to six circuits. Causes of circuit defects that may arise during synthesis are quantified first. A procedure is then developed to identify the segments of Burmester curves which produce mechanisms with all precision positions on the same circuit. The procedure is applicable to any Stephenson linkage.

Circuit Rectification for Four Precision Position Synthesis of Four-Bar and Watt Six-Bar Linkages

The circuit defect arises in precision position based linkage synthesis when a potential solution linkage cannot be moved between all precision positions without disassembly. Circuit rectification consists of reducing the potential solution space to include only those linkages that are free of the circuit defect. Circuit rectification for four precision position synthesis of Watt six-bar linkages is developed here. Circuit rectification of four-bar linkages is refined in the process. An example demonstrates the synthesis of a new Watt I sofa bed linkage free of the circuit defect.

The Application of Geometric Constraint Programming to the Design of Motion Generating Six-Bar Linkages

This paper looks at the application of Geometric Constraint Programming (GCP) to the synthesis of six-bar planar linkages. GCP is a synthesis method that relies on the built-in geometric capabilities of commercial solid-modeling programs to produce linkage designs while operating in the “sketch” mode for these programs. GCP provides the user with the opportunity to create mechanisms in their entirety at multiple design positions.The complexity of analyzing potential defects (such as circuit or branch defects) within a six-bar mechanism poses significant challenges to the user who might try to design such a mechanism in a single step. The methods presented in this paper apply GCP in a stepwise manner to create six-bar linkages that are less likely to suffer from defects than if they were created in a single step. Stepwise approaches are presented for six-bar mechanisms designed to solve a problem involving rigid-body guidance (motion generation). The linkages considered include the Stephenson I, II, and III chains, as well as the Watt I six-bar. The Watt II six-bar is not included since this mechanism’s application to rigid-body guidance can be handled by GCP methods previously developed for four-bar linkages.Copyright

An Examination of Trispiral Hinges Suitable for Use in ABS-Based Rapid Prototyping of Compliant Mechanisms

This paper examines the use of a trispiral hinge in compliant mechanisms generated by low cost, ABS-based, rapid prototyping machines. Hinges are examined to establish relationships between hinge geometry parameters (core radius, spiral angle, spiral pitch, and spiral thickness) and hinge performance (in-plane rotation, off-axis stability). A number of joint parameter combinations are found that provide good joint rotation characteristics with minimal off-axis instability. These joints allow for joint rotations up to ±90 degrees from a neutral position with little parasitic motion during the rotation. The implementation of these joints is further examined through the building and testing of fully compliant mechanisms based on the Roberts and Hoeken approximate straight-line mechanism geometries. The fully compliant mechanisms are shown to have the ability to closely recreate the approximate straight-line motion of the equivalent 4-bar chains. As such, the trispiral joint provides promise as a joint type that can be used effectively in conjunction with fused deposition modeling (FDM) machines that use ABS as the build material.Copyright

Preliminary Investigations Into the Design and Manufacturing of Fully Compliant Layered Mechanisms (FCLMs)

The relatively new technology of additive manufacturing (also known as “3-D printing” or “rapid prototyping”) presents some intriguing possibilities for the design of compliant mechanisms. This paper introduces a new category of compliant mechanisms — Fully Compliant Layered Mechanisms (FCLMs) — that rely on additive manufacturing to produce mechanisms with complex geometry. An FCLM is a fully compliant mechanism whose geometry requires two or more links to cross over one another to achieve a desired motion. The need to have crossing links requires the mechanism to have multiple layers. Such a mechanism is fairly easy to produce using additive manufacturing systems, but the more brittle materials associated with additive manufacturing also impose some limitations on the design of FCLMs. This paper presents an overview of some of these limitations along with approaches that are being developed to solve the challenges of using additive manufacturing in the production of compliant linkages. The focus is on lumped compliant mechanisms with key challenges that include: the selection of a proper joint type; the layering of the compliant mechanism; and the stability of the mechanism. Beam type joints such as a spiral joint are found to be suitable for use with additive manufacturing. These joints have some lateral instability which can be reduced by proper layering and structural reinforcements in the mechanism. These joints also pose the potential for increased parasitic motion, which can be minimized by joint design approaches. Preliminary ideas are presented for the solution of these problems along with some needs for future development.Copyright

Mixed Exact and Approximate Position Design of Planar Linkages via Geometric Constraint Programming (GCP) Techniques

The synthesis of mechanisms to reach multiple positions can often be satisfied by the specification of a combination of exact and approximate positions. Geometric Constraint Programming (GCP) uses industry standard parametric modeling software to obtain solutions to planar synthesis problems. This paper demonstrates the capability of GCP to solve problems that contain a combination of exact and approximate positions. The approximate positions are added to existing GCP design approaches by the application of geometric constraints to locate moving points on a mechanism within specified circular target zones. The target zones are used to guide the coupler point of a linkage along an approximate path between critical precision positions. The approach applies to the synthesis of both four-bar and complex linkages. In complex linkages, the target zones can be applied to multiple points on the linkage to better coordinate the motion of one or more floating links with the overall mechanism motion. The methods presented in the paper focus on the use of 2 exact positions plus 2–3 approximate positions. Examples are provided for the solution of rigid-body guidance problems for both four-bar and six-bar linkages. As with many GCP solutions, the graphical solutions presented are well within the capabilities and understanding of both undergraduate students and the practicing engineer.Copyright

Parametric Modeling: A New Paradigm for Mechanisms Education?

The evolution of engineering education is driven, in part, by the tools available. This paper examines how a relatively new tool, that of parametric modeling, can be implemented in the presentation of an introductory course in the design and analysis of mechanisms. The combined graphical and computational power of a parametric modeling system provides an ideal starting point to introduce a variety of common concepts. This paper examines how parametric modeling can be used to analyze mechanism mobility (including degrees-of-freedom, Grashof type, transmission angles, and limits of motion), and velocity (including mechanical advantage) in planar linkages. The use of parametric modeling as a tool for teaching linkage synthesis is also reviewed.The primary purpose of the paper is to briefly demonstrate the power of parametric modeling and how this tool can form a foundation for mechanism education. The ability to rapidly create and change parametric sketches of mechanisms allows the student much more opportunity to study “what if” scenarios and recognize trends in mechanism analysis and design. The visual and interactive nature of the tool also has excellent compatibility with the highly computer literate background of the modern student. Parametric modeling has the necessary capability to become the paradigm for mechanisms instruction in the 21st century.Copyright

Instantaneous power methods to improve the inertial characteristics of planar linkages

Abstract High speed linkages may take advantage of the inertia of one or more floating links to improve the mechanisms operation. The center of gravity of the floating link(s) can be located to produce an inertia force that is acting in the same direction as the velocity vector of the center of gravity. The instantaneous power that results from this alignment helps the linkage move through a position that would typically require a higher driving torque.