Transactions of the Canadian Society for Mechanical Engineering

Volume 30 (2006), Issue 4

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This work presents a technique for synthesizing adjustable planar, five-bar motion generators to approximate prescribed rigid-body positions and satisfy rigid-body positions with prescribed tolerances. This method is an extension of the adjustable planar five-bar motion generation method introduced by the authors (1). By incorporating rigid-body point tolerances in the rigid-body displacement matrices, the calculated circle and center point curves of the five-bar mechanism become circle and/or center point regions. From these regions, fixed and moving pivots for the five-bar mechanism can be selected that approximate the prescribed rigid-body positions and satisfy rigid-body positions with prescribed tolerances. The example in this work considers two-phase moving pivot adjustments in the planar five-bar motion generator.

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The main objective of this paper is to present a theoretical approach to model the vibro-acoustic behavior of flat sandwich composite panels. Two models are studied: symmetrical laminate composite and sandwich composite panel. The theories are developed in a wave approach context. It is shown that a discrete layers sandwich composite panel modeling type leads to a 12th order relation of dispersion while a laminate composite panel modeling leads to a 6th order relation of dispersion. The two models give similar results at low frequencies but the modeling of a sandwich panel using the laminate panel theory leads to inaccuracies at high frequencies. The dispersion relations are first solved in the context of generalized polynomial complex eigenvalues problems. Next, the dispersion relations are used to derive the analytical expression of the critical frequencies and to calculate the natural frequencies of the panel. Using the dispersion relation's solutions, the study is then focused on the numerical computation of the group velocity, the modal density and the total transmission loss.

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In this paper, the concept that adds the interior nodes of the Lagrange elements to the serendipity elements is described and a family of enriched elements is presented to improve the accuracy of finite element analysis. By the use of the static condensation technique at the element level, the extra computation time in using these elements can be ignored. Three-dimensional elastic problems are used as examples in this paper. The numerical results show that these enriched elements are more accurate than the traditional serendipity elements. The convergence rate of the enriched elements is the same as the traditional serendipity elements. In the numerical example, the error norm of the first order enriched elements can be reduced when compared with the use of the traditional serendipity element, but the computation time is increased a little. The use of enriched second and third order hexahedral elements does not only improve accuracy, but also saves the computation time for solving the system of equations, when the precondition conjugate gradient method is used to solve the system of equations. The saving of computation time is due to the decrease in the number of iteration for the iteration method.

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A novel approach to gear design to produce so-called Logix gears is based on differential geometric methods and results in higher order contact parameters, i.e., reduced stress concentration. Profiles designed in this way admit concave-to-convex mating tooth surfaces and a simple two gear set with such properties is presented as an example. Once a pair of mating gears has been configured it is then shown how to design bobbing racks to cut these gears.

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The paper proposes a method for the synthesis of planar mechanisms, where a combination of cams and linkages is used in order to improve the kinematic behaviour of mechanical presses. The purpose is to synthesize a function generating mechanism, with a constant input-velocity, able to move the press ram according to an optimal law of motion. The proposed synthesis methodology consists of two phases. As a first step, a linkage type-synthesis is performed, based on the mobility the generation task requires. An initial multi degree-of-freedom (d.o.f.) mechanism is thus selected. One or more disc cams are then synthesized in order to reduce the system's mobility and to obtain a single-input combined mechanism. The final system is able to generate a specific input/output relationship, as defined by any number of precision configurations. In order to optimize the synthesis process, according to dimensional and kinematical criteria, a genetic algorithm is employed. A goal function is defined on the basis of both performance criteria and design rules, and minimized by means of evolutionary theory. The proposed methodology is applied to the kinematic optimization of mechanical presses for deep drawing and precision cutting processes.

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Automated model generation and solution for motion planning and re-planning of robotic systems will play an important role in the future reconfigurable manufacturing systems. Solving the inverse kinematic problem has always been the key issue for computer-controlled robots. Considering the large amount of similarities that exist among the industrial 6R robotic systems, this work classifies them into two main types (Puma-type and Fanuc-type) and then provides a unified geometric solution based on a unified kinematic structure called Generic Puma-Fanuc (GPF) model. A widespread study of different kinematic groups originating from eleven robot manufacturers made it possible to develop the GPF model that can be reconfigured according to the D-H rules (Denavit, and Harteriberg1). A graphical interface by which the robot kinematic model is represented and the D-H parameters are auto-generated for use in solving the inverse kinematic problem. A generic solution module called Unified Kinematic Modeler and Solver (UKMS) implements the geometric approach for solving the inverse kinematic problem. The outcomes are then employed for robot control. Numerical examples are presented for exploring the solution capabilities of our unified approach.

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The paper presents the validation of a methodology for the optimal synthesis of a planar mechanical system able to reproduce knee kinematics in a limited range of motion. Such a mechanism could be effectively used in the design and placement of a moving external fixator for the knee joint articulation in either post-traumatic and pathological treatment or rehabilitation. The purpose is to help patient's recovery through a limited and occasional movement of the articulation without loading the injured area. In order to validate the actual method, knee kinematics is estimated by means of plane radiographs of the articular joint of an healthy volunteer at different flexion angles. Each of the lateral radiographs shows the relative tibia-femur motion in different configurations. The whole movement is reconstructed by interpolation, assuming a relative gliding law. Geometric synthesis, based on Burmester's theory, is thus used to identify a set of compatible four-bar-linkages (f.b.l.), which reproduce the estimated rigid body motion.

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Extension of a recently developed analytical two-phase steam flow calculator to high pressure cases is performed in this paper. The initial solution, obtained in earlier study was developed for low pressure cases. In low pressure cases, the vapor portion of the two-phase mixture reliably obeys the ideal gas Equation of State (EOS). In the present high pressure study, real gas effects are included using the more suitable EOS of "Lee-Kesler". The model similar to the low pressure model assumes local equilibrium between the phases, in which condensation onsets as soon as the saturation line is closed. Before the condensation onset, the stagnation properties echo those at the inflow. However, beyond the condensation onset, the transfer of latent heat toward the vapor portion of the two-phase mixture rises its stagnation temperature. To evaluate this rise in the vapor portion stagnation temperature, a non dimensional parameter ζ is defined. Comparison for low- and high-pressure cases between the present analytical solution and the published experimental values in the literature show very good agreement.