Sushrut G. Bapat

Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model Concept

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of static equilibrium equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end boundary conditions, depending on the locations of the effecting force and/or displacement boundary conditions. A unique solution may exist when a third beam end boundary condition is specified; however, this selection is not unconditional. A deflection domain concept is proposed to assist with the selection of the third boundary condition in a more realistic manner.Copyright

On a Generalized Approach for Design of Compliant Mechanisms Using the Pseudo-Rigid-Body Model Concept

This paper provides a generalized approach for the design of compliant mechanisms. The paper discusses the implicit uncoupling, between the kinematic and energy/torque equations, enabled by the pseudo-rigid-body model concept, and utilizes it for designing a variety of compliant mechanism types for a wide-range of user specifications. Pseudo-rigid-body four-bar mechanisms, with one to four torsional springs located at the revolute joints, are considered to demonstrate the design methodology. Mechanisms are designed for conventional tasks, such as function, path and motion generation, and path generation with prescribed timing, with energy/torque specified at the precision-positions. State-of-the-art rigid-body synthesis techniques are applied to the pseudo-rigid-body model to satisfy the kinematic requirements. Energy/torque equations are then used to account for the necessary compliance according to the user specifications. The approach utilizes a conventional, simple yet efficient optimization formulation to solve energy/torque equations that allow a designer to i) achieve realistic solutions, ii) specify appropriate energy/torque values, and iii) reduce the sensitivities associated with the ‘synthesis with compliance’ approach. A variety of examples are presented to demonstrate the applicability and effectiveness of the approach. All of the examples are verified with the finite element software ANSYS®.Copyright

Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model (PRBM) Concept

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of static equilibrium equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end boundary conditions, depending on the locations of the effecting force and/or displacement boundary conditions. A unique solution may exist when a third beam end boundary condition is specified; however, this selection is not unconditional. A deflection domain concept is proposed to assist with the selection of the third boundary condition in a more realistic manner.Copyright

Mechanical Advantage of a Compliant Mechanism and Significant Factors Affecting it, Using the Pseudo-Rigid-Body Model Approach

Although work related to mechanical advantage of compliant mechanisms has been presented almost two decades ago, unlike many rigid-body mechanism systems, this performance measure has seldom been used. In great part, the reasons are attributed to, one, the relatively recent development of and a lack of familiarity with this technology and, two, the complexity of the understanding and evaluation of mechanical advantage of compliant systems. In an effort to simplify the evaluation, this work uses the pseudo-rigid-body model (PRBM) of a compliant mechanism, along with traditional notions of power conservation and angular velocity ratios using instant centers. As a first step, the inherent compliance in the mechanism is neglected in determining its mechanical advantage, followed by considerations to optimize its structural configuration for enhancing its mechanical advantage. The PRBM methodology, which offers us a way to estimate the characteristic compliance of the mechanism, now enables its inclusion in determining the mechanical advantage of the compliant mechanism. Two significant factors affecting it are i) the structural configuration of the PRBM, and ii) the energy stored in compliant elements of the mechanism. Several case studies are presented, which suggest that minimizing the latter contribution relative to that of an optimized structural configuration may improve the mechanical advantage of a compliant mechanism. Nonetheless, its effect on the mechanical advantage cannot be neglected.Copyright

Characteristic Deflection Domain for Various Compliant Segment Types, and its Importance in Compliant Mechanism Synthesis and Analysis

Compliant mechanism design inherently requires certain specified displacement boundary conditions to be satisfied. Obtaining realistic solutions for such problem types often becomes a challenge as the number of displacement boundary condition specifications increases. Typically, related failures are attributed to the numerical nature of the solution process. Little attention has been given to the fundamental understanding of the deformation behavior of flexible continuum with respect to its limits of mobility or reach. This paper strives to provide an insight into this aspect of compliant mechanism design. To assist a designer with the specification of realistic and achievable requirements, the concept of characteristic deflection domain has been proposed in the past. This paper systematically develops the characteristic deflection domain for a variety of compliant segment types. The pseudo-rigid-body model (PRBM) representation is utilized for determining the lower and upper boundaries of the deflection domain. The paper further investigates the mobility characteristics of compliant mechanisms comprised of multiple segment types. Case studies are presented that help exemplify the use of the characteristic deflection domain plots. The results suggest that the number, type, and orientation of the compliant segments have a significant effect on the mobility of compliant mechanisms. Thus, care must be exercised by the designer when specifying free-choices/boundary conditions in compliant mechanisms synthesis and analysis.Copyright

A Method for a More Accurate Calculation of the Stiffness Coefficient in a Pseudo-Rigid-Body Model (PRBM) of a Fixed-Free Beam Subjected to End Forces

The pseudo-rigid-body model (PRBM) concept allows compliant mechanisms to be modeled using existing knowledge of rigid-body mechanisms, thereby considerably simplifying their analysis and design. The PRBMs represent the compliant segments with two or more rigid-body segments, connected using pin joints (characteristic pivots). The beam compliance is modeled using a torsional spring placed at the characteristic pivot, whose spring constant K is evaluated using a pseudo-rigid-body parameter termed as the beam stiffness coefficient. This paper presents a method to more accurately calculate the beam stiffness coefficient for a fixed-free compliant beam subjected to a combination of horizontal and vertical forces. The improved stiffness coefficient (KΘ) expressions are derived as a function of the pseudo-rigid-body angle, Θ and the load factor, n. To exemplify the application of the improved results, the expressions derived are successfully implemented in modeling a fixed-guided beam with an inflection point, allowing it to be modeled as two fixed-free beams pinned at the inflection point.Copyright

On a Compliant Mechanism Design Methodology Using the Synthesis with Compliance Approach for Coupled and Uncoupled Systems

Compliant mechanisms are defined as those that gain some or all of their mobility from the flexibility of their members. Suitable use of pseudo-rigid-body models for compliant segments, and state-of-the-art knowledge of rigid-body mechanism synthesis types, greatly simplifies the design of compliant mechanisms. Starting with a pseudo-rigid-body four-bar mechanism, with one to four torsional springs located at the revolute joints to represent mechanism characteristic compliance, a simple, heuristic approach is provided to develop various compliant mechanism types. The synthesis with compliance method is used for three, four and five precision positions, with consideration of one to four torsional springs, to develop design tables for standard mechanism synthesis types. These tables reflect the mechanism compliance by specification of either energy or torque. The approach, while providing credible solutions, experiences some limitations. The method is not yet robust, and research is continuing to further improve it. Examples are presented to demonstrate the use of weakly or strongly coupled sets of kinematic and energy/torque equations, as well as different compliant mechanism types in obtaining solutions.