Study On A Two Degrees Of Freedom Closed-loop Propulsive Mechanism Based On Spatial Linkage Inspired From Frog’s Hindlimbs

The design of biomimetic propulsion mechanism is the key technology to realize the efficient movement of robots in both water and land environments.Compared with the open-loop propulsion mechanism,the closed-loop propulsion mechanism has the advantages of simple structure,small inertia and simple control.In nature,frogs swim in water and crawl on land mainly through their hind limbs.This bionic property provides a biological template for the design of bionic propulsion mechanism.In this paper,the frog hind limb is taken as the bionic template,combined with the spatial linkage mechanism,the novel water and land propulsion mechanism with less freedom is studied,aiming at simplifying the complexity of the mechanism while preserving the efficient propulsion effect.The research includes the configuration design of the frog hind limb propulsion mechanism,the analysis of the frog hind limb propulsion mechanism with two degrees of freedom,the scale synthesis of the frog hind limb propulsion mechanism and the function verification of the propulsion mechanism.(1)Configuration design of frog hind leg propulsion mechanism.Taking the hind limb of frog as the biomimetic template,the hind limb function in the process of frog swimming and crawling is analyzed and simplified.Combined with the closed-loop mechanism design,two configurations of 7R-RSCR and 7R-RSUR with swimming function and 7R-RSCP and 7RRSUP with crawling function are proposed.The proposed spatial mechanism is a two-degreeof-freedom closed-loop mechanism.The degree of freedom of the whole mechanism is analyzed based on screw theory.By simulating frog’s swimming gait with swimming propulsion mechanism,the estimated underwater propulsion force model is established based on the blade element theory,and the relationship between input parameters and output propulsion force is analyzed.The crawling mechanism is used to mimic the crawling motion of frogs,while the model of propulsive step length is established.The relationship between input actuation and output displacement of the propulsive mechanism is analyzed.The rationality of the configuration design of the two-DOF spatial linkage mechanism for mimicking frog’s hind limbs is verified by the functional analysis in both aquatic and terrestrial environments.(2)Mechanical analysis of the bionic propulsion mechanism with two degrees of freedom.The two-degree-of-freedom propulsion mechanism is composed of Watt Ⅰ type planar six-bar linkage chain and a single-loop spatial linkage chain with single degree of freedom.According to the geometric characteristics of the planar six-bar mechanism,an explicit model of the positive position analysis of the planar six-bar mechanism is proposed,which reduces the computational difficulty and avoids the multi-solution characteristic of the general solution.Based on the forward model of explicit position,the forward model of velocity and acceleration of the six-bar mechanism is derived,and the motion characteristics of the six-bar mechanism are analyzed.Based on the closed vector method,the forward and backward solution models,velocity models and acceleration models of the RSCR,RSUR,RSCP and RSUP spatial mechanisms are established,and the input-output characteristics of the position,velocity and acceleration of the single-loop spatial mechanisms are obtained.In the analysis of single-loop spatial mechanism,according to the geometric characteristics of RSCR and RSCP configurations,an explicit model of forward position solution was constructed to reduce the difficulty of forward position solution.(3)Dimensional synthesis of frog hind limbs.The body guidance synthesis method is used to optimize the mechanism parameters.Based on the kinematic model of the proposed propulsive mechanism,an equal square polynomial system is constructed for Watt type I planar six-bar mechanism,and the homotopy method is used for the numerical solutions.Aiming at solving the problems of the body guidance synthesis of Watt Ⅰ type six-bar linkage such as extremely complex computation and large computation cost,a novel fast solution method is proposed.The optimization model is constructed,and the interior point method is implemented to solve the constrained nonlinear optimization model,and the dimensional parameters satisfying the design objectives are obtained successively.On the basis of determining the parameters of the planar six-bar mechanism,the small-scale models of the parameters of the RSCR,RSUR,RSCP and RSUP single-loop spatial mechanism are constructed.The dimensional parameters of the mechanism are obtained by solving polynomial systems.Thus,the optimal design of the overall mechanism is completed.(4)Function verification of frog-like crawling mechanism and swimming mechanism.Rapid prototyping based on 3D printing technology.Based on the specific gait,the step length and yaw angle performance of the crawling mechanism were tested to verify the rationality of the mechanism design.The crawling step of the test mechanism is 4 times of the lateral displacement,and the yaw Angle is reduced to 3.2°.For the propulsion mechanism swimming underwater,a propulsion test platform is built to test the propulsion force generated in the propulsion phase during swimming underwater,and compare it with the resistance generated on the foot in the gliding phase and recovery phase.The underwater propulsion performance of the mechanism is tested.The peak underwater thrust is about 10 times of the resistance in the recovery phase.The mechanism is designed to enhance peak thrust while minimizing drag during propulsion.Further explore the simplified design of bionic mechanism,design soft underwater propulsion mechanism based on dielectric high elastic polymer,and compare with the closed-loop spatial linkage,analyze the application potential of soft underwater propulsion mechanism designed based on dielectric elastic polymers.