The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2...The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.展开更多
The aim of this article is to detect the detachment between the cam and the follower using the largest Lyapunov exponent parameter,the power density function of fast Fourier transform,and Poinarémaps due to the n...The aim of this article is to detect the detachment between the cam and the follower using the largest Lyapunov exponent parameter,the power density function of fast Fourier transform,and Poinarémaps due to the nonlinear dynamics phenomenon of the follower.The detachment between the cam and the follower was investigated for different cam speeds and different internal distances of the follower guide from inside.This study focuses on the use of the cam–follower system with a bionic quadruped robot through a linkage mechanism.Multishock absorber(spring–damper–mass)systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower.The SolidWorks program was used in the numerical solution,while a high‐speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to identify the follower position.The friction and impact were considered between the cam and the follower and between the follower and its guide.In general,when the cam and the follower are in permanent contact,there is no loss in potential energy,and no impact or restitution.The detachment between the cam and the follower increases with increasing coefficient of restitution in the presence of the impact.展开更多
文摘The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.
文摘The aim of this article is to detect the detachment between the cam and the follower using the largest Lyapunov exponent parameter,the power density function of fast Fourier transform,and Poinarémaps due to the nonlinear dynamics phenomenon of the follower.The detachment between the cam and the follower was investigated for different cam speeds and different internal distances of the follower guide from inside.This study focuses on the use of the cam–follower system with a bionic quadruped robot through a linkage mechanism.Multishock absorber(spring–damper–mass)systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower.The SolidWorks program was used in the numerical solution,while a high‐speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to identify the follower position.The friction and impact were considered between the cam and the follower and between the follower and its guide.In general,when the cam and the follower are in permanent contact,there is no loss in potential energy,and no impact or restitution.The detachment between the cam and the follower increases with increasing coefficient of restitution in the presence of the impact.
