1,721,008 research outputs found
A pseudo-rigid body model based on finite displacements and strain energy
No full textDuring the last decades, the modeling of flexures undergoing large deflections has been the subject of many investigations. Various rigid body models have been proposed in an effort to reproduce with high accuracy the path followed by the free-end section of the flexible element. Systems with multiple degrees of freedom have been also presented considering the possible occurrence of an inflection point. However, as the number of DoFs increases, optimization techniques must be implemented to define the characteristic parameters. In this investigation, a one-DoF rigid body model is developed focusing on the pole of the displacements associated to the poses of the free-end section. Two different cases are analyzed, depending on whether the pole is a proper point or an improper point. Strain energy is evaluated to calculate the stiffness coefficients of the rigid body model. Considering end moments and combined loads, two different formulations are elaborated to achieve analytical and numerical solutions, respectively. The proposed model is load dependent and provides an exact solution of the modeling problem, both in the case of rotation and in the case of translation of the free-end section. Occurrence of an inflection point is also considered and various examples are presented
Analysis of the center of rotation in primitive flexures: Uniform cantilever beams with constant curvature
No full textPrecision of rotation is a fundamental characteristic of primitive flexures, especially when compliant mechanisms are designed for micro-scale applications. In case of single leaf flexures, distributed compliance allows flexible beams to undergo large deflections. Nevertheless, the center of rotation changes its position during such deflections. In this paper, large deflection analysis is performed on cantilever beams with uniform cross section and constant curvature, subjected to end-moment loads. Analytical expressions to determine the position of the center of rotation of the flexure are derived. The center of rotation refers to the displacement of the free-end section of the beam, occurring when the flexure, due to the external load application, moves from its neutral configuration to the deformed one. Several examples are considered and the analytical solutions are compared to the results obtained by finite element analysis. A final example focuses on the determination of the pseudo-rigid body model
High-order kinematics of uniform flexures
No full textIn the last decades, many efforts have been made to analyze and model small and large deflections of flexures, considering complex load cases and different solution techniques. However, few investigations focused on the kinematic aspects related to the deflection analysis of the flexible elements, and limited the study to the second-order kinematics. In this paper, an analytical formulation based on the instantaneous geometric invariants is developed to give deep kinematic insight, up to the fourth order, into the motion generated by the deflections. The problem is addressed from a geometrical point of view, defining the fundamental geometric entities that characterize the motion, that are inflection circle, cubic of stationary curvature and its derivative, Ball’s point, and Burmester’s points. Thanks to these special points on the plane, straight and circular paths can be approximated to the third and to the fourth order, respectively. The proposed formulation defines the geometric characteristics of flexures with different curvatures. An application regarding the definition of pseudo-rigid body models is discussed. Finite element simulations are performed to validate the results
Effect of initial curvature in uniform flexures on position accuracy
No full textPosition accuracy is a prerequisite for compliant mechanisms, especially in micro-scale applications. Generally, this feature depends on the flexures ability to imitate the revolute joints of the pseudo-rigid body model. In case of flexible elements, the center of the relative rotation varies its position during the deflections, affecting the position accuracy. In this paper, the role played by the initial curvature is investigated, in case of uniform primitive flexures. Analytical expressions are derived to evaluate the shift of the rotation axis with respect to the flexure centroid. An example shows the performance of four flexures with different curvatures, evaluated by comparing the rotation axis shift and the position error
Delineation of management zones based on soil mechanical-chemical properties to apply variable rates of inputs throughout a field (VRA)
No full textSingle-point synthesis of compliant mechanisms
No full textIn the last decades, several methods have been developed for the synthesis of compliant mechanisms. Generally, the proposed approaches work at the mechanism level, leading to the definition of a compliant structure starting from specific design requirements and constraints. In this paper, a novel point compliance synthesis method for planar systems is presented. The method relies on a different perspective, namely, at the output port level. It starts from the requirements on an already defined compliant structure, modeled as a two-port system, and leads to the design of the suspended body, that serves both as input and output port. The kinetostatics of the elastic suspension is described by resorting to the ellipse of elasticity theory, under the assumptions of linear deflections and linear elastic material. Then, the point compliance synthesis, based on spectral analysis, targets the field of displacements of the suspended body to define the points meeting the design requirements. The synthesis problem is formulated as a non-dimensional algebraic system that always admits real solutions. In particular, the obtained closed-form expressions hold in the general case, for every compliant mechanism. The method is applied to two case studies, at the element and at the mechanism levels, and finite element simulations are performed to test the theoretical results
Comparison of Distributed-Order and Fractional-Order PID with symmetric Bode plot for position control of inertial loads
No full textProjective synthesis of planar compliant mechanisms
No full textIn this paper, a novel method for the synthesis of planar compliant mechanisms, based on projective geometry, is presented. The projective synthesis method exploits the antiprojective polarity in the weighted projective plane, enabling the extension of single-point to single-body relations. The method consists of a top-down procedure that, starting from the load–displacement requirements, defines the elastic suspension as a system of substructures in series and parallel arrangements, according to the prescribed topology. The geometric decomposition intrinsically guarantees positive definiteness of the kinetostatic relations at any level. Multiple solutions to the synthesis problem can be generated. The method has been implemented to the synthesis of compliant mechanisms with open and closed chains, and numerical simulations have been performed to validate the theoretical model
ACCURACY OF INITIALLY-CURVED CROSS-AXIS FLEXURAL PIVOTS
No full textAccuracy of the cross-axis flexural pivot is a fundamental requirement in a variety of applications, from robotics to precision engineering. Many studies have been conducted to improve this feature by investigating the effects of various geometric parameters of the cross-axis pivot, such as orientation of the flexures and position of the intersection point. In the present study, the rotational performance is improved by considering two different features. The first one consists in defining an arrangement based on the position of the flexure centroids, instead of considering the position of their intersection point. The second one consists in introducing an initial curvature for the flexible elements. The constraints introduced by these features lead to the definition of a geometry characterized by two degrees of freedom, that is developed for the design of the curved cross-axis flexural pivot. Different layouts are introduced and nonlinear numerical simulations are carried out to evaluate the pivot accuracy. In particular, accuracy is compared to the one of the straight cross-axis flexural pivot by introducing a proper parameter, based on the determination of the pole of the finite displacements. The results are presented as accuracy design maps, useful to define the geometric layout meeting the accuracy requirements
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