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Compliant mechanisms are usually joint-less and mono- lithic structural elements which can transfer energy, force, and displacement via elastic deformation. The compliance is one unique feature which makes compliant mechanisms to be adaptive in a limited range during operation. Topology optimization is a numerical method to optimize material lay- out within a given design space, and is one major approach for synthesis of compliant mechanisms. An optimal layout of compliant mechanism can be identified from an initial design domain with pre-specified loading conditions. The finite element discretization of the analysis domain is usu- ally the first step for topology optimization methods. After mesh generation, different numerical algorithms can be applied to optimize the design via the concept of gradually removing inefficient elements from the analysis domain. The iterative result is expected to evolve into an optimal topology under certain boundary conditions. The element removal scheme [1–3] in topology optimization can be classified into two categories, which are hard-kill and soft-kill approaches. The hard-kill method directly removes inefficient elements from the analysis domain, whereas the soft- kill method defines a very small value for either elastic modulus or density to those unnecessary elements. In addition to the traditional one way element removal approaches, the bi-directional evolutionary structural optimization (BESO) [3–6] method and SERA method [7, 8] allow elements to be removed and added simultaneously in each iteration. The usage of a numerical filter scheme is one general approach for topology optimization to avoid the numerical instabilities such as mesh-dependency and checkerboard problem [1–3, 9, 10]. For example, the filter scheme in the BESO method [3–6] defines the filtered elemental sensitivity numbers based on the calculation of the nodal sensitivity numbers and weight factors (defined by the fil- ter radius between specific node and element) to ensure the existence of a continuous layout of the analyzed structure The nodal sensitivity numbers are not with any physical meaning on their own [3] and are defined by averaging the elemental sensitivity numbers of corresponded connecting elements. In addition, the usage of the numerical springs [6–8, 11–19] at targeted input and output locations of the analyzed compliant mechanism is one popular method to better identify the hinge-free layout in synthesis of com- pliant mechanisms. Due to the existence of the numerical springs, the displacements in the global analysis domain are usually quite small thus the linear finite element formulation can be used in topology optimization. The global stiffness matrix in the finite element method for topology optimization can be obtained by assembling the elemental stiffness matrix times the pseudo density of each element with a penalty factor plus the numerical spring matrix [19].
There are many applications in synthesis of compliant mechanisms via topology optimization, including the development of the planar compliant parallel mechanism [20], constant force mechanism [21], actuators [21–25], and compliant grippers [26–28]. In addition to the general finite element-based topology optimization methods, other approaches such as the genetic algorithm based load path synthesis approach [27] is also proposed to search for feasible topologies for single-input single-output compliant gripper mechanism; while this method can ensure the structural connectivity and create designs that are free of gray areas, one limitation of this approach is that the results may contain overlapping elements due to the nature of the load path generation. In robotic grasping, the development of the robotic hands [29–32] or grippers [28, 33–37] for dexterous manipulation and shape adaption is one challenging task in robotics. While the robotic hands are usually more human- like designs with high dexterity, the grippers are relatively simpler mechanisms. A dexterous robotic hand or gripper usually requires to have several degrees of freedom for actuation, which may lead to significant contribution to the weight, complexity, and overall dimensions of the design. To resolve this issue, the underactuated mechanism, which implies a mechanism has fewer actuators than its degrees of freedom, becomes promising especially for the applications of the underactuated compliant mechanism. In industrial automation, the grasping process is one of the fundamental tasks which move the objects to the following processing line by using the grippers. Comparing to traditional grippers with rigid links and joints, passively underactuated complaint grippers have several advantages such as being light weight, less expensive to manufacture comparing to rigid- joint mechanisms, and most importantly, the flexibility to adapt various objects with different sizes and shapes. Nor- mal compliant grippers usually can handle objects with a small size variation range. For handling objects with larger size and shape variations, the development of the passive adaptive compliant gripper (ACG) [28, 36] becomes one emerging issue for this application. In addition, the compliance and adaptability of the compliant graspers can prevent possible damage of the geometrically inconsistent objects being handled, which is a particularly important issue for handling of natural food products [38–40] and live poultry in food processing industry [41–43].
This study aims to develop an innovative underactuated ACG to maximize output displacement for fast grasping of irregular objects. Both topology and size optimization methods are used in design of the ACG. In order to increase the computational efficiency for traditional hard-kill and soft- kill topology optimization methods, an efficient soft-add topology optimization method is presented in this study to synthesize the optimal topology of the ACG. One special characteristic of the soft-add scheme is that the elements are equivalent to be numerically added into the analysis domain. As the target volume fraction constraint for topology optimization of compliant mechanism is usually lower than 30% of the given design domain, traditional methods which remove inefficient elements from 100% to target volume fraction are inefficient. The optimal design process includes topology optimization and size optimization. The concept design of the optimal layout of the ACG can be obtained from topology optimization process, then the detailed dimensions of the ACG can be determined from size optimization process. The size optimization method used in this study is a mixed method incorporating Augmented Lagrange Multiplier (ALM) method [44], Simplex method [44], and nonlinear finite element analysis. In addition, the dynamic performance and contact behavior of the ACG are analyzed by using the commercial explicit dynamic finite element analysis solver, LS-DYNA, which has been increasingly used to analyze flexible multibody dynamic problems involving contact [42, 43, 45–47]. After the numerical investigation, three designs of the ACG are prototyped. The experimental tests are performed to verify the designs. The outcomes of this study provide numerical methods for design and analysis of compliant mechanisms with better computational efficiency, as well as to develop an innovative compliant gripper for fast grasping of unknown objects.