In this paper, a space-time absolute nodal coordinate formulation cable (SAC) element forming technique based on the Lagrange family of shape functions is proposed. Two distinct SAC elements, each with a distinct spatial shape function, have been generated by this method. Moreover, the external forces such as the bending moment and the air resistance formula have been accounted for. The Lagrange multiplier method, along with the concepts of replacement constraint and supplementary constraint, has been employed to provide a solution for the dynamics of constrained mechanical systems. Additionally, a constraint conversion strategy has been suggested. The solver has been constructed through Hamilton’s law of varying action. The space-time finite element method is used to solve dynamic problems, employing the Newton algorithm and quasi-Newton algorithm. The accuracy and efficiency of the solution has been verified by three simulations and one experiment. The circle-bending static simulation and the double-ended velocity impact dynamic simulation demonstrate the accuracy of the two elements. The correlation between statics and dynamics has been studied for different discretization methods and different solvers’ calculation accuracy and efficiency. Different modeling methods, time steps, order and the application of the quasi-Newton method all have a bearing on the efficiency of the solution. Finally, a comparison with an experiment in the free-pendulum simulation reveals the capability of this model to simulate dynamic problems with air resistance.

The overrunning clutch, or freewheel, is a kind of universal part with a one-way drive character, and is widely used in machinery. Typical roller overrunning clutches and sprag overrunning clutches have shortcomings such as low load bearing capacity, low torsional stiffness, and short life. For these reasons, studies on high-performance overrunning clutches have always been the focus of researchers. In this paper, a new type of double arc sprag overrunning clutch is proposed that overcomes the disadvantages of poor transmission capacity and low rigidity found in traditional overrunning clutches. The mechanical model of the double arc sprag overrunning clutch is established, the calculation formulas of the overrunning clutch engagement conditions and overrunning conditions are deduced, and the forces of the outer ring, roller, and inner star wheel of the overrunning clutch are also deduced. The contact stress and transmission torque of the overrunning clutch are compared with those of the roller overrunning clutch and the sprag overrunning clutch. The results show that the proposed overrunning clutch has the largest load capacity, which is 5.75 times that of the roller type overrunning clutch, and 2.1 times that of the sprag type overrunning clutch. The experiment shows that the proposed overrunning clutch has reliable bonding conditions in the oil-free and oil-immersed state, and the overrunning condition is sensitive, which indicates the effectiveness of the double arc sprag overrunning clutch. The roller overrunning clutch and double arc sprag overrunning clutch with the same geometric parameters are designed and manufactured, and the torsional stiffness test of the three types of overrunning clutches is carried out. The results show that the torsional stiffness of the double arc sprag overrunning clutch is the largest, which is 4.6 times of the roller overrunning clutch and 6.2 times of the sprag overrunning clutch.

The construction of high-order shape function is a key and difficulty for unstructured grid mesh and sliding boundary problem. In this paper, a construction method of space-time absolute nodal coordinate formulation quadrilateral cable (SACQ) is proposed and the accuracy of SACQ element is studied and verified with 3 different applications. First, the shape function of SACQ is constructed with spatiotemporal reduction coordinate and the action integral of SACQ is composed with Lagrangian function and discrete with perspective transformation. second, numerical convergence region is discussed and determined with Courant number. Furthermore, a space-time nodal dislocation and its relation with Courant number is studied. The simulation and verification are focusing on some realistic problems. Finally, one-sided impact, free-flexible pendulum, taut string with sliding boundary and a deployable guyed mast under impact transverse wave are simulated. In these problems, unstructured grid meshed with SACQ has similar energy convergence and accuracy with structured grid but shows better efficiency.