Compliant Mechanisms: Implementation of Topological Optimization Method for the Development of Robotic Gripper with Flexible Finger

Micro and nano positioning stages are critically important to both the mechanical and electronic industries. Gripping micro objects are required for a wide range of important applications such as the assembly of micro-parts to obtain miniature systems or component assembly in electronics packages. An effective mechanical micro and nano manipulator should possess the ability to grasp objects of different shapes steadily with high positioning accuracy. A microgripper compliant mechanism is one of the key elements in micro-robotics and micro-assembly technologies for handling micro-objects without damage. Compliant mechanisms can play an important role in the design of micro- devices for micro-electro-mechanical systems (MEMS) applications. Compliant mechanisms are flexible structures, which can generate the desired motions by undergoing elastic deformation instead of through rigid linkage/joints as in rigid body mechanisms. The topology optimization methods search for an ideal material distribution of a structure. In this paper, topology optimization method is applied for designing a three- dimension compliant microgripper mechanism. The optimal topology configuration of the compliant microgripper mechanism is demonstrated. This compliant mechanism can be used to handle a wide range of micro and nano objects up to 400μm.

Purpose – This paper aims to show an evolutionary topology optimization procedure for the design of compliant electro-thermal mechanisms. Design/methodology/approach – The adopted methodology is based in the evolutionary structural optimization (ESO) method. This approach has been successfully applied by this group for compliant mechanisms optimization under directly applied input loads and simple thermal loads. This work proposes an extension of this procedure, based on an additive version of the method, to solve the more complicated case of electro-thermal actuators optimum design, based on Joule's resistive heating. Findings – Examples solved for the design of plane compliant mechanisms are presented to check the validity of this technique. The designs obtained are compared favorably with results obtained by other authors to illustrate and validate the method, showing the viability of this technique for the optimization of compliant mechanisms under electro-thermal actuation. Research limitations/implications – This investigation is based on and additive version of the evolutionary method. Since this approach does not have the capability to remove material it could be combined with the classic element rejection evolutionary method to overcome these deficiencies, developing an improved bi-directional algorithm, which should be analyzed and applied for these types of designs in future works. Practical implications – Electro-thermal actuators have widespread use in MicroElectroMechanical Systems applications. Since these elements cannot be manufactured using typical assembly processes compliant mechanisms optimization play a crucial role for their successful design. The proposed methodology could help engineers to rapidly conceive complex and efficient actuators. Social implications – The topology optimization procedure developed in this paper enables systematic design of these devices, which can result in a save of manufacturing time and cost. Originality/value – Most applications of the ESO method have considered maximum stiffness structure design, and even if it has been successfully applied to some other optimum material distribution problems, electro-thermal actuators design has not been considered yet. This paper shows that this methodology could be useful also in the design of electro-thermal compliant mechanisms, and provides engineers with a very simple and practical alternative design tool.

This paper presents a new topology optimization method of spatial compliant parallel mechanism. The constant motion transmission characteristic matrix of a special parallel mechanism is analyzed. Combining the matrix with topology optimization, a new multi-objective topology optimization formula of multiple input and output compliant mechanism is proposed. The strategy is capable of optimizing the compliant mechanism free of considering the replacement of rigid hinges by flexible ones, so as to obtain a compliant mechanism with higher motion accuracy and there is a linear mapping relationship between input and output. Through several numerical examples, it is verified that the compliant mechanism obtained by this method is isomorphic with the original parallel mechanism in kinematics.

SUMMARYThis paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm. Copyright © 2011 John Wiley & Sons, Ltd.

Topology optimization of a spatial compliant parallel mechanism based on constant motion transmission characteristic matrix

Buckling-induced instability in topology optimization of compliant constant-force mechanisms

The object of this study is to develop a topology optimization method for the design of joint compliant mechanism structures. Joint compliant mechanisms are compliant mechanisms consisting of rigid or sufficiently rigid one-dimensional elements and elastic hinge joints. Although continuumbased methods have been successful to configure compliant mechanisms, the optimized mechanisms are usually difficult to manufacture because of their geometric complexities. The ground structure based topology optimization method using beam elements can alleviate the geometric complexity issue, but it is still difficult to actually fabricate the optimized layouts. Existing topology optimization results on compliant mechanisms indicate that optimized compliant mechanisms have very localized eastic deformations to wok as mechanisms. This means that most elastic deformations in compliant mechanisms occur in very localized hinge regions. Therefore, it will be advantageus to find directly the elastic hinge joint locations and stiffnss values by a topology optimization formulation while ground beams are treated only as joint-connecting elements without going through much deformation. Motivated by this observation, we propse a joint stiffness controlling method where gournd beams of given thickness are connected through joint springs at beam joints. The main characteristics of the proposed method are: 1) beam elements are connected by elastic joints, not by rigid ones, 2) instead of geometric dimensions of beam elements, the stiffness of the joints is varied during optimization, 3) the maximum translational and rotational stiffnesses of the joints are assumed to be proportional to those of neighboring beams, and 4) the final topology of a structure is obtained by considering the connectivity of beam elements at the joints. To take manufacturability into account, joint springs are allowed to take on only a few discrete values; a set of pre-manufactured elastic joints having different rotational stiffness are assumed to be available in designing compliant mechanisms. The validity and effectiveness of the proposed design method is investigated by solving a couple of numerical examples including the popular design problems of a micro force converter and micro gripper.

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

Optimal design method for 3-DOF planar compliant mechanisms based on mapping matrix constraints

A new topology optimization method for planar compliant parallel mechanisms

ABSTRACTThe synthesis of compliant mechanisms (CMs) is frequently achieved through topology optimization. Many synthesis approaches simplify implementation by assuming small distortions, but this limits their practical application since CMs typically undergo large deformations that include geometric and material nonlinearities. CMs designed to generate a desired deformation path at the output points under specific loads are known as path‐generating CMs. However, these CMs face significant challenges in topology optimization, resulting in the development of only a few optimization methods. Existing approaches often include only certain load cases in the optimization process. Consequently, if a CM designed this way encounters different load cases in practice, its path‐generating behavior cannot be guaranteed. The authors have previously contributed to the development of an approach suitable for synthesizing load case‐insensitive CMs. This paper extends that approach to account for nonlinearities, enabling the synthesis of path‐generating CMs. The effectiveness of this extended approach is demonstrated through appropriate design examples. Additionally, the paper presents, for the first time, a shape‐adaptive path‐generating CM.

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.

PurposeThe purpose of this paper is to describe an element addition strategy for topology optimization of thermally actuated compliant mechanisms under uniform temperature fields.Design/methodology/approachThe proposed procedure is based on the evolutionary structural optimization (ESO) method. In previous works, this group of authors has successfully applied the ESO method for compliant mechanism optimization under directly applied input loads. The present paper progresses on this work line developing an extension of this procedure, based on an additive version of the method, to approach the more complicated case of thermal actuators.FindingsThe adopted method has been tested in several numerical applications and benchmark examples to illustrate and validate the approach, and designs obtained with this method are compared favorably with the analytical solutions and results derived by other authors using different optimization methods, showing the viability of this technique for uniformly heated actuators optimization.Research limitations/implicationsAs a simple initial approach, this research considers only uniform heating of the system, while many thermal actuators are heated nonuniformly. Future works will be based on electrothermal actuation, and nonuniform Joule heating will be considered as well, which might lead to more elegant and efficient solutions.Practical implicationsCompliant micromechanisms that are responsible for movement play a crucial role in microelectromechanical systems (MEMS) design, which cannot be manufactured using typical assembly processes and may not make use of traditional hinges or bearings. The topology optimization method described in this paper enables the systematic design of these devices, which can result in reduced conception time and manufacturing cost.Originality/valueThe ESO method has been successfully applied to several optimum material distribution problems, but not for thermal compliant mechanisms. Even if most applications of this method have been oriented for maximum stiffness structure design, this paper shows that this computation method may be also useful in the design of thermal compliant mechanisms and provides engineers with a very simple and practical alternative design tool.

Design of compliant mechanisms considering thermal effect compensation and topology optimization

Piezoelectric actuators have the obvious advantages of simple and compact structure, high precision and long stroke. However, it is difficult to satisfy the various industrial requirements. Topology optimization method can be used to find the new configurations of the compliant mechanism, and different objective function and constraint conditions can be flexibly used to determine the compliant mechanism. In the research of piezoelectric actuators, due to the advantages of compact structure, no lubrication and large displacement magnification, compliant mechanism is extremely suitable to be introduced into the design of piezoelectric actuators. In recent years, topology optimization method is frequently used to design the compliant mechanism on piezoelectric actuator, and has become a research hotspot. In this chapter, the development of topology optimization method is introduced, the design and research on the compliant mechanism of piezoelectric actuator have been summarized, and the future research direction and challenges of topology optimization design for flexure hinge type piezoelectric actuators are prospected.