A Building Block Approach for the Design of Statically Balanced Compliant Mechanisms

2009 ◽  
Author(s):  
Karin Hoetmer ◽  
Just L. Herder ◽  
Charles J. Kim
Keyword(s):  
Building Block ◽  
Force Feedback ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Negative Stiffness ◽  
High Fidelity ◽  
Input Output ◽  
Input And Output ◽  
Block Approach

Particularly when high-fidelity force feedback is required, such as in surgical forceps, the energy loss between input and output in compliant mechanisms is undesired. To restore the force feedback, the principle of static balancing can be applied, where a balancing segment with a negative stiffness is added to a compliant mechanism. Currently there are no mature methods for the design of statically balanced compliant mechanisms (SBCM). The goal of this paper is to investigate the possibility of extending the Building Block Approach for the design of statically balanced compliant mechanisms. To this end, the Building Block Approach is extended with negative stiffness balancing building blocks that can be added to a designed compliant mechanism. To demonstrate the feasibility of the method, a statically balanced compliant gripper was designed by this Extended Building Block Approach. The maximum operating force of the unbalanced gripper of 3.5 N was reduced to −1 N for the balanced gripper. Thus, the gripper is slightly overbalanced. The gripper example demonstrates the functionality of the proposed method; the input-output stiffness of a compliant mechanism can be severely reduced by a balancing segment.

Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Karin Hoetmer ◽  
Geoffrey Woo ◽  
Charles Kim ◽  
Just Herder
Keyword(s):  
Force Feedback ◽  
High Efficiency ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Negative Stiffness ◽  
High Fidelity ◽  
Proof Of Concept ◽  
Design Considerations ◽  
Design And Testing

In some applications, nonconstant energy storage in the flexible segments of compliant mechanisms is undesired, particularly when high efficiency or high-fidelity force feedback is required. In these cases, the principle of static balancing can be applied, where a balancing segment with a negative stiffness is added to cancel the positive stiffness of the compliant mechanism. This paper presents a strategy for the design of statically balanced compliant mechanisms and validates it through the fabrication and testing of proof-of-concept prototypes. Three compliant mechanisms are statically balanced by the use of compressed plate springs. All three balanced mechanisms have approximately zero stiffness but suffer from a noticeable hysteresis loop and finite offset from zero force. Design considerations are given for the design and fabrication of statically balanced compliant mechanisms.

Functional Characterization of Compliant Building Blocks Utilizing Eigentwists and Eigenwrenches

2008 ◽  
Author(s):  
Charles J. Kim
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Deformable Body ◽  
Functional Characterization ◽  
Building Blocks ◽  
Future Research ◽  
Special Cases ◽  
Block Approach

Compliant mechanisms are devices which utilize the flexibility of their constituent members to transmit motion and forces. Unlike their rigid body counterparts, compliant mechanisms typically contain no traditional joints. The focus of this research is the development of a building block approach for the synthesis of compliant mechanisms. Building block methods better facilitate the augmentation of designer intuition while offering a systematic approach to open-ended problems. In this paper, we investigate the use of the eigentwists and eigenwrenches of a deformable body to characterize basic kinematic function. The eigentwists and eigenwrenches are shown to demonstrate parametric behavior when applied to the compliant dyad building block, and in special cases may be compared to compliance ellipsoids. The paper concludes by articulating future research in a building block approach to compliant mechanism synthesis.

A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Charles J. Kim ◽  
Yong-Mo Moon ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Single Point ◽  
Rapid Prototype ◽  
Building Blocks ◽  
Single Input Single Output ◽  
Kinematic Behavior ◽  
Insight Into ◽  
Block Approach

In this paper, we investigate a methodology for the conceptual synthesis of compliant mechanisms based on a building block approach. The building block approach is intuitive and provides key insight into how individual building blocks contribute to the overall function. We investigate the basic kinematic behavior of individual building blocks and relate this to the behavior of a design composed of building blocks. This serves to not only generate viable solutions but also to augment the understanding of the designer. Once a feasible concept is thus generated, known methods for size and geometry optimization may be employed to fine-tune performance. The key enabler of the building block synthesis is the method of capturing kinematic behavior using compliance ellipsoids. The mathematical model of the compliance ellipsoids facilitates the characterization of the building blocks, transformation of problem specifications, decomposition into subproblems, and the ability to search for alternate solutions. The compliance ellipsoids also give insight into how individual building blocks contribute to the overall kinematic function. The effectiveness and generality of the methodology are demonstrated through two synthesis examples. Using only a limited set of building blocks, the methodology is capable of addressing generic kinematic problem specifications for compliance at a single point and for a single-input, single-output compliant mechanism. A rapid prototype of the latter demonstrates the validity of the conceptual solution.

Conceptual Synthesis of Compliance at a Single Point

2006 ◽  
Author(s):  
Charles Kim ◽  
Yong-Mo Moon ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanism ◽  
Single Point ◽  
Geometry Optimization ◽  
Building Blocks ◽  
Kinematic Behavior ◽  
The Mathematical Model ◽  
Insight Into ◽  
Block Approach

In this paper, we investigate a methodology for the conceptual synthesis of compliance at a single point based on a building block approach. The methodology lays the foundation for more general compliant mechanism synthesis problems involving multiple points of interest (i.e. inputs and outputs). In the building block synthesis, the problem specifications are decomposed into related sub-problems if a single building block cannot perform the desired task. The sub-problems are tested against the library of building blocks until a suitable building block is determined. The synthesized design is composed of an assembly of the building blocks to provide the desired functionality. The building block approach is intuitive and provides key insight into how individual building blocks contribute to the overall function. We investigate the basic kinematic behavior of individual building blocks and relate this to the behavior of a design composed of building blocks. This serves to not only generate viable solutions but also to augment the understanding of the designer. Once a feasible concept is thus generated, known methods for size and geometry optimization may be employed to fine tune performance. The key enabler of the building block synthesis is the method of capturing kinematic behavior using Compliance Ellipsoids. The mathematical model of the compliance ellipsoids facilitates the characterization of the building blocks, transformation of problem specifications, decomposition into sub-problems, and the ability to search for alternate solutions. The compliance ellipsoids also give insight into how individual building blocks contribute to the overall kinematic function. The effectiveness and generality of the methodology are demonstrated through a synthesis example. Using only a limited set of building blocks, the methodology is capable of addressing generic kinematic problem specifications.

Design Synthesis of 2-D Compliant Mechanisms Utilizing Serial Concatenation of Building Blocks

2009 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Unique Point ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Parametric Variation ◽  
Point Of Interest

In this section we implement a characterization based on eigen-twists and eigen-wrenches for the deformation of a compliant mechanism at a given point of interest. For 2-D mechanisms, this involves characterizing the compliance matrix at a unique point called the center of elasticity. At the center of elasticity, the translation and rotational compliances are decoupled. We give an intuitive graphical understanding of compliance at this point by representing the translational compliance as an ellipse and the coupling between the translational and rotational parameters as vectors (Coupling vectors). This representation gives us an intuitive understanding of series and parallel combination of building blocks. We obtain a parametric variation of these quantities for a compliant dyad building block, and show with examples how a mechanism can be synthesized by a combination of building blocks to obtain desired deformation requirements. We also propose a combination of series and parallel concatenation to achieve more than one specification simultaneously. Such a characterization can be extended to synthesize involving multiple ports.

Towards the Design of a Statically Balanced Compliant Laparoscopic Grasper Using Topology Optimization

2008 ◽  
Author(s):  
Ditske J. B. A. de Lange ◽  
Matthijs Langelaar ◽  
Just L. Herder
Keyword(s):  
Topology Optimization ◽  
Force Feedback ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Negative Stiffness ◽  
Compensation Mechanism ◽  
Laparoscopic Grasper ◽  
The Difference ◽  
Force Displacement ◽  
Compliant Mechanism Design

This paper presents the design of a grasping instrument for minimally invasive surgery. Due to its small dimensions a compliant mechanism seems promising. To obtain force feedback, the positive stiffness of the compliant grasper must be statically balanced by a negative-stiffness compensation mechanism. For the design of compliant mechanisms, topology optimization can be used. The goal of this paper is to investigate the applicability of topology optimization to the design of a compliant laparoscopic grasper and particularly a compliant negative-stiffness compensation mechanism. In this study, the problem is subdivided in the grasper part and the compensation part. In the grasper part the deflection at the tip of the grasper is optimized. This results in a design that has a virtually linear force-displacement characteristic that forms the input for the compensation part. In the compensation part the difference between the force-displacement characteristic of the grasper part and the characteristic of the compensation part is minimized. An optimization problem is formulated enabling a pre-stress to be incorporated, which is required to obtain the negative stiffness in the compensation part. We can conclude that topology optimization is a promising approach in the field of statically balanced compliant mechanism design, even though there is great scope improvement of the method.

A Lumped-Model Based Building-Block Concatenation for a Conceptual Compliant Mechanism Synthesis

2008 ◽  
Author(s):  
Girish Krishnan ◽  
Charles Kim ◽  
Sridhar Kota
Keyword(s):  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Building Blocks ◽  
Mechanical Efficiency ◽  
Size Optimization ◽  
Lumped Model ◽  
Storage Mechanism ◽  
Conceptual Designs ◽  
Motion Characteristics

Present building-block synthesis techniques for compliant mechanisms [4–7] account for the kinematic behavior of the mechanism alone, leaving the stiffness, manufacturability and mechanical efficiency to be determined by the shape-size optimization process. In this effort, we aim to generate practical and feasible conceptual designs by designing for kinematics and stiffness simultaneously. To enable this, we use a lumped spring-lever model, which intuitively characterizes the stiffness and the kinematics of a deformable-complaint building block with distinct input and output points. This model aids in the understanding of how the stiffness and the kinematics of building blocks combine when concatenated to form a mechanism. We use this understanding to synthesize compliant mechanisms by combining building blocks of known motion characteristics. A simple compliant-dyad building block is characterized for its lumped values of stiffness and kinematics. The concatenation of these dyad-building blocks is solved in detail, and guidelines for conceptual synthesis are proposed. Two practical examples are solved; a motion amplifier for a piezo-stack and a compliant energy storage mechanism for a staple-gun. The conceptual designs obtained from this approach are very close to the kinematic and the stiffness requirements of the application, thus minimizing the role of shape and size optimization to achieve the problem specification. The model, when extended to higher dimensions may be used to solve for precision positioning and other applications.

An Instant Center Approach Toward the Conceptual Design of Compliant Mechanisms

2005 ◽  
Vol 128 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Charles J. Kim ◽  
Sridhar Kota ◽  
Yong-Mo Moon
Keyword(s):  
Conceptual Design ◽  
Building Block ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometry Optimization ◽  
Building Blocks ◽  
Cross Sectional ◽  
Rigid Body Model ◽  
Cross Sectional Size

As with conventional mechanisms, the conceptual design of compliant mechanisms is a blend of art and science. It is generally performed using one of two methods: topology optimization or the pseudo-rigid-body model. In this paper, we present a new conceptual design methodology which utilizes a building block approach for compliant mechanisms performing displacement amplification/attenuation. This approach provides an interactive, intuitive, and systematic methodology for generating initial compliant mechanism designs. The instant center is used as a tool to construct the building blocks. The compliant four-bar building block and the compliant dyad building block are presented as base mechanisms for the conceptual design. It is found that it is always possible to obtain a solution for the geometric advantage problem with an appropriate combination of these building blocks. In a building block synthesis, a problem is first evaluated to determine if any known building blocks can satisfy the design specifications. If there are none, the problem is decomposed to a number of sub-problems which may be solved with the building blocks. In this paper, the problem is decomposed by selecting a point in the design space where the output of the first building block coincides with the second building block. Two quantities are presented as tools to aid in the determination of the mechanism's geometry – (i) an index relating the geometric advantage of individual building blocks to the target geometric advantage and (ii) the error in the geometric advantage predicted by instant centers compared to the calculated value from FEA. These quantities guide the user in the selection of the location of nodes of the mechanism. Determination of specific cross-sectional size is reserved for subsequent optimization. An example problem is provided to demonstrate the methodology's capacity to obtain good initial designs in a straightforward manner. A size and geometry optimization is performed to demonstrate the viability of the design.

An Instant Center Approach to the Conceptual Design of Compliant Mechanisms

2004 ◽  
Author(s):  
Charles J. Kim ◽  
Sridhar Kota ◽  
Yong-Mo Moon
Keyword(s):  
Conceptual Design ◽  
Building Block ◽  
Design Methodology ◽  
Compliant Mechanisms ◽  
Geometry Optimization ◽  
Quantitative Measure ◽  
Building Blocks ◽  
Rigid Body Model ◽  
Base Mechanism ◽  
Block Approach

The conceptual design of compliant mechanisms is generally performed using one of two methods: topology optimization or the Pseudo-Rigid-Body Model. In this paper, we present a conceptual design methodology which utilizes a building block approach. The concept of the instant center is developed for compliant mechanisms and is used to characterize the building blocks. The building block characterization is used in guiding the problem decomposition. The compliant four-bar building block is presented as a base mechanism for the conceptual design. The geometric advantage is used as a quantitative measure to guide the designer in determining the shape of the building block. An example problem demonstrates the methodology’s capacity to obtain viable conceptual designs in a straightforward manner. Resulting mechanisms satisfy initial kinematic requirements and are ready for further refinement using size and geometry optimization.

scholarly journals Fully-compliant statically-balanced mechanisms without prestressing assembly: concepts and case studies

2011 ◽  
Vol 2 (2) ◽  
pp. 169-174 ◽  
Author(s):  
G. Chen ◽  
S. Zhang
Keyword(s):  
Stress Relaxation ◽  
Force Feedback ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
High Fidelity ◽  
Constant Force ◽  
Force Transmission ◽  
Actuation Force ◽  
New Concepts ◽  
Creep And Stress Relaxation

Abstract. The purpose of this paper is to present new concepts for designing fully-compliant statically-balanced mechanisms without prestressing assembly. A statically-balanced compliant mechanism can ideally provide zero stiffness and energy free motion like a traditional rigid-body mechanism. These characteristics are important in design of compliant mechanisms where low actuation force, accurate force transmission or high-fidelity force feedback are primary concerns. Typically, static balancing of compliant mechanisms has been achieved by means of prestressing assembly. However, this can often lead to creep and stress relaxation arising in the flexible members. In this paper two concepts are presented which eliminate the need for prestressing assembly of compliant mechanisms: (1) a weight compensator which employs a constant-force compliant mechanism, (2) a near-zero-stiffness mechanism which combines two multistable mechanisms. In addition to the advantages provided by statically-balanced compliant mechanisms, two other notable features of these statically-balanced mechanisms are their ability to be monolithically fabricated and to return to their as-fabricated position without any disassembly when not in use.

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