Development of Commercial Quality Software for Mechanisms Design Education

Development of high quality technical software in a university environment has been a persistent problem since the introduction of educational software to institutions of higher learning. Design software presents a number of special considerations. It differs significantly from other types of educational software in that it requires a free-form creative environment rather than a question-and-answer format or even a detailed analysis of a fixed set of specified problems. Ideally, the student should be able to explore a wide range of realistic problems and develop both optimal and non-optimal solutions using a variety of mechanisms. This paper outlines the differences between truly “commercial quality” software and that developed for use at the local campus and explores the difficulties involved in producing such a product. Users drastically underestimate the amount of manpower and funding required to develop software packages on a par with widely available applications such as AutoCAD, WordPerfect, or Lotus 1-2-3. Similarly, design education software developed at universities for national distribution represent thousands of man-hours of development and may be the work of a single individual or a team of programmers led by a faculty member.

Issues on Teaching Kinematics and Mechanism Design

The issues, problems and possible solutions involved in teaching a modern course on mechanisms and kinematics are addressed from the perspective of a professor and a student. A historical examination shows the value of modern (computer) solution of classical dilemmas. The structure of an introductory course is then presented, with comments on its educational attributes. The solution of several design problems with LINCAGES©, a computer software package, demonstrates the prowess of the modem student/computer liaison.

Geometric Characteristics of the Center-Point Curve Based on the Kinematics of the Compatibility Linkage

In this paper we develop a method of characterizing the center-point curves for planar four-position synthesis. We predict the five characteristic shapes of the center-point curve using the kinematic classification of the compatibility linkage obtained from a complex number formulation for planar four-position synthesis. This classification scheme is more extensive than the conventional Grashof and non-Grashof classifications in that the separate classes of change point compatibility linkages are also included. A non-Grashof compatibility linkage generates a unicursal form of the center-point curve; a Grashof compatibility linkage generates a bicursal form; a single change point compatibility linkage generates a double point form; and a double or triple change point compatibility linkage generates a circular-degenerate or a hyperbolic-degenerate form.

A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms

A generalized accuracy performance synthesis methodology for planar closed chain mechanisms is proposed. The relationship between the sensitivity to variations of link lengths and the location of the moving pivots of four-link mechanisms is investigated for the particular objective of three and four position synthesis. In the three design positions case, sensitivity maps with isosensitivity curves plotted in the design solution space allow the designer to synthesize a planar mechanism with desired sensitivity value or to optimize sensitivity from a set of acceptable design solutions. In the case of four design positions, segments of the Burmester design curves that exhibit specified sensitivity to link length tolerance are identified. A performance sensitivity criterion is used as a convenient and a useful way of discriminating between many possible solutions to a given synthesis problem.

Grashof Type Rotatability Criteria of Spherical Five-Bar Linkages

In this paper rotatability criteria of spherical five bar linkages are analytically derived. First an equivalent linkage in which sum of any two link lengths is less than π is found and then rotatability criteria of spherical 5 bar linkage are developed for this linkage. The rotatability criteria developed in this paper are stated as follows: The two input angles are completely revolvable if and only if in the equivalent linkage the sum of the longest and the two shortest links is less than the sum of the remaining two links and there is one and only one long link between each pair of noninput angles (long link being any link excluding the shortest links). It is also shown that an angle θ included by two links αi and αj is completely revolvable if and only if the sum of the longest link and shorter of αj and αj is less than or equal to the sum of the remaining three links.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

Nonlinear Optimal Design of Dynamic Mechanical Systems

Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

Tool Path Geometry for Multi-Axis Kinematics Conversion in CAD-CAM Integration

In the integration of CAD and CAM, it is necessary to relate machine tool kinematics and control in a CAM process to the geometrical data in a CAD model. The data stored in a CAD model is usually static in nature and represented by unitless parameters. Yet, in machine tool motion and control, the data should be transformed into a time dependent domain. In this paper, a general theory on the conversion from desired paths to motion trajectory is analytically derived. The geometrical properties of a desired path, including position, tangent, and curvature are related to the kinematics of coordinated motion including feedrate, acceleration, and jerk. As a result, the motion commands used as control references to track arbitrary space curves for five-axis computer-controlled machines can be generated in a rather straight-forward as well as systematic way.

A Proposed Method to Group the Solutions From Dimensional Synthesis: Planar Triads for Six Precision Position

In this paper, a method has been proposed to group into six sets the infinite number of solutions from dimensional synthesis of planar triads for six precision positions. The proposed method reveals the relationships between the different configurations of the compatibility linkage and the sets of numerical solutions from dimensional synthesis. By checking the determinant signs and the contunities of values of the sub-Jacobian matrices and their derivatives with respect to the independent angular displacement for all constraint sets in the compatibility linkage, it enables the computer to identify and group the synthesized solutions. Numerical examples have been given to verify the applicability of this method. Six sets of the partial triad Burmester curves have been plotted based on grouped solutions. Suitable solutions can be easily found from the partial triad Burmester curves and utilized for the prescribed design task. This method provides a useful tool to group the dimensional synthesis solutions and enhances the computer automation in the design of linkage mechanisms.

On the Design of Planar and Spherical Pure-Rolling Indexing Cam Mechanisms

A new design of indexing cam mechanisms for parallel and intersecting shafts is presented here in a unified framework, so that both pure rolling and positive motion are achieved. Power losses due to Coulomb friction are eliminated, while producing motions free of jerk discontinuities. The pressure angle is anlyzed and applied to define the positive motion.