Understanding and analyzing large and nonlinear deflections are the major challenges of designing compliant mechanisms. Initially, curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross section, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM), which is termed as the chained BCM (CBCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

Tristable actuators can achieve state retention without energy input and switch states when the external energy reaches the jump threshold. Among many designs, a tristable actuator that can switch between two stable states without passing through the third state is highly beneficial for multimode robots. In this work, a design scheme of a novel tristable actuator is proposed under the inspiration of tristate gate circuit. Switching between any two of the three stable states in such a tristable actuator is realized when we orthogonalize two bistable structures that can be driven by artificial muscle materials. A kinetostatic model using the chained beam constraint model is established to characterize the actuator design. Experimental results validate the kinetostatic model and the effectiveness of the actuator. To demonstrate the functionality, a robotic crawler combining two tristable actuators is prototyped, which is capable of functions of bidirectional crawling as well as an in-situ reboot to locomotion after a fall, by utilizing the tristable switching feature.

The fusion of temporal consistency and semantic information with limited foreground information for background segmentation using deep learning is an underinvestigated problem. In this paper, we explore the relation between temporal consistency and semantic information based on the law of total probability. A highly concise framework is proposed to fuse these two types of information. A theoretical proof is given to show that the proposed framework is more accurate than either the temporal consistency-based model or the semantic information-based model and that each model is a special case of the proposed framework. The proposed framework is a white-box framework that can easily be embedded into a deep neural network as a merging layer. In the proposed model, only a few parameters must be learned, which substantially reduces the need for a large dataset. In addition, these interpretable parameters reflect our understanding of the background and can be applied to a wide range of environments. Extensive evaluations indicate the promising performance of the proposed method. Our code and trained weights for the experiments are available at GitHub. ^{1 1}https://github.com/zengzhi2015/SS_TC_BS (We encourage the reader to run the program for a better understanding of the proposed method).