Repository logo

On Advancing the Topology Optimization Technique to Compliant Mechanisms and Robots




Journal Title

Journal ISSN

Volume Title




Degree Level



Compliant mechanisms (CMs) take advantage of the deformation of their flexible members to transfer motion, force, or energy, offering attractive advantages in terms of manufacturing and performance over traditional rigid-body mechanisms (RBMs). This dissertation aims to advance the topology optimization (TO) technique (1) to design CMs that are more effective in performing their functions while being sufficiently strong to resist yield or fatigue failure; and (2) to design CMs from the perspective of mechanisms rather than that of structures, particularly with the insight into the concepts of joints, actuations, and functions of mechanisms. The existing TO frameworks generally result in CMs that are much like load-bearing structures, limiting the applications of CMs. These CMs (1) do not have joints, (2) are actuated by a translational force, and (3) can only do simple work such as amplifying motion or gripping. Three TO frameworks for the synthesis of CMs are proposed in this dissertation and they are summarized below. First, a framework was developed for the design of efficient and strong CMs. The widely used stiffness-flexibility criterion for CM design with TO results in lumped CMs that are intrinsically efficient in transferring motion, force, or energy but are prone to high localized stress and thus weak to resist yield or fatigue failure. Indeed, distributed CMs may have a better stress distribution than lumped CMs but have the weakness of being less efficient in motion, force, or energy transfer than lumped CMs. Based on this observation, the proposed framework rendered the concept of hybrid systems, hybrid CMs in this case. Further, the hybridization was achieved by a proposed super flexure hinge element and a design criterion called input stroke criterion in addition to the traditional stiffness-flexibility criterion. Both theoretical exploration and CM design examples are presented to show the effectiveness of the proposed approach. The proposed framework has two main contributions to the field of CMs: (1) a new design philosophy, i.e., hybrid CMs through TO techniques and (2) a new design criterion—input stroke. Second, a systematic framework was developed for the integrated design of CMs and actuators for the motion generation task. Both rotary actuators and bending actuators were considered. The approach can simultaneously synthesize the optimal structural topology and actuator placement for the desired position, orientation, and shape of the target link in the system while satisfying the constraints such as buckling constraint, yield stress constraint and valid connectivity constraint. A geometrically nonlinear finite element analysis was performed for CMs driven by a bending actuator and CMs driven by a rotary actuator. Novel parameterization schemes were developed to represent the placements of both types of actuators. A new valid connectivity scheme was also developed to check whether a design has valid connectivity among regions of interest based on the concept of directed graphs. Three design examples were constructed and a compliant finger was designed and fabricated. The results demonstrated that the proposed approach is able to simultaneously determine the structure of a CM and the optimal locations of actuators, either a bending actuator or a rotary actuator, to guide a flexible link into desired configurations. Third, the concept of a module view of mechanisms was proposed to represent RBMs and CMs in a general way, particularly using five basic modules: compliant link, rigid link, pin joint, compliant joint, and rigid joint; this concept was further developed for the unified synthesis of the two types of mechanisms, and the synthesis approach was thus coined as module optimization technique—a generalization of TO. Based on the hinge element in the finite element approach developed at TU Delft (Netherlands in early 1970), a beam-hinge model was proposed to describe the connection among modules, which result in a finite element model for both RBMs and CMs. Then, the concept of TO was borrowed to module optimization, particularly to determine the “stay” or “leave” of modules that mesh a design domain. The salient merits with the hinge element include (1) a natural way to describe various types of connections between two elements or modules and (2) a provision of the possibility to specify the rotational input and output motion as a design problem. Several examples were constructed to demonstrate that one may obtain a RBM, or a partially CM, or a fully CM for a given mechanical task using the module optimization approach.



Compliant Mechanisms, Topology Optimization, Mechanism Design



Doctor of Philosophy (Ph.D.)


Mechanical Engineering


Mechanical Engineering




Part Of