The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Tensegrity mechanisms (TM) are well-appraised for their compliance and lightweight, making their design theory a hot research topic recently. However, due to unconstrained DOFs, the design and analysis of TMs are generally more complicated than traditional mechanisms composed of rigid links and joints. A compact 3-DOF tensegrity manipulator is introduced and an advanced two-step kinematic modeling method is proposed in this paper. This method is first assumed that bars and cables are rigid to estimate the equilibrium state using the energy-based method. Then, the flexibility of bars and cables is considered, and the force density method equations are solved utilizing the equilibrium state obtained by the previous step as the initial guess of iteration for fast computation. Based on the two-step method, the performances of the TM, such as workspace, manipulability, potential energy, and stiffness, are analyzed. Thereafter, the installation position and size of the manipulator are optimized under the workspace constraint. In the optimization process, discrete points on the prescribed task workspace contour are used to simplify the constraint to improve computational efficiency. Finally, study cases are investigated to validate the proposed method, and the feasibility of the discrete sampling method for constraint simplification is also verified.

Antenna panels of a satellite are usually deployed and supported by a deployable mechanism. The accuracy of the deployable mechanism is important because it directly affects the performance of the satellite. This article focuses on the accuracy analysis of a deployable antenna considering the coupled effects of joint clearances and link tolerances, and based on which, two accuracy synthesis methods are further discussed. A novel geometric error modeling method is proposed to estimate the error space of the outer panel of the antenna. The advantages of the proposed method are that it can handle the overconstrained constraints efficiently and decouple the positioning error and orientation error. Moreover, the error space is visualized using a sampling method. Based on the proposed error modeling method, the maximum orientation and positioning errors are computed, and following which, sensitives of the antenna accuracy to tolerances considering various sizes of clearances are analyzed. Finally, two optimization methods for accuracy synthesis are discussed, and instructive conclusions are drawn.