All-position robots are widely applied in the welding of complicated parts.Welding of intersecting pipes is one of the most typical tasks.The welding seam is a complicated saddle-like space curve,which puts a great ch...All-position robots are widely applied in the welding of complicated parts.Welding of intersecting pipes is one of the most typical tasks.The welding seam is a complicated saddle-like space curve,which puts a great challenge to the pose planning of end-effector.The special robots designed specifically for this kind of tasks are rare in China and lack sufficient theoretical research.In this paper,a systematic research on the pose planning for the end-effectors of robot in the welding of intersecting pipes is conducted. First,the intersecting curve of pipes is mathematically analyzed.The mathematical model of the most general intersecting curve of pipes is derived,and several special forms of this model in degraded situations are also discussed.A new pose planning approach of bisecting angle in main normal plane（BAMNP） for the welding-gun is proposed by using differential geometry and the comparison with the traditional bisecting angle in axial rotation plane（BAARP） method is also analytically conducted.The optimal pose of the welding-gun is to make the orientation posed at the center of the small space formed by the two cylinders and the intersecting curve to help the welding-pool run smoothly.The BAMNP method can make sure the pose vertical to the curve and center between the two cylinders at the same time,therefore its performance in welding-technique is superior to the BAARP method.By using the traditional BAARP method,the robot structure can become simpler and easier to be controlled,because one degree of freedom（DOF） of the robot can be reduced.For the special case of perpendicular intersecting,an index is constructed to evaluate the quality of welding technique in the process of welding.The effect of different combination of pipe size on this index is also discussed.On the basis of practical consideration,selection principle for BAARP and BAMNP is described.The simulations of those two methods for a serial joint-type robot are made in MATLAB,and the simulation results are consistent to the analys展开更多
The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio(ρ ...The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio(ρ 0 ?0. 8). Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable toρ 0(R/T)1/2 ?1, is used for the analysis of the shell with cutout. The solution in terms of displacement function for the nozzle with a nonplanar end is based on the Goldenveizer equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates (α, β) on the shell, or Gaussian coordinates (ζ, θ) on the nozzle into three-di-mensional cylindrical coordinates(ρ,θ, z). Their expressions on the intersecting curve are periodic functions ofθ and expanded in Fourier series. Every harmonic of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature. The results obtained are in agreement with those from the three-dimensional finite element method and experiments.展开更多
Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we det...Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.展开更多
The automatic cutting of intersecting pipes is a challenging task in manufacturing.For improved automation and accuracy,this paper proposes a model-driven path planning approach for the robotic plasma cutting of a bra...The automatic cutting of intersecting pipes is a challenging task in manufacturing.For improved automation and accuracy,this paper proposes a model-driven path planning approach for the robotic plasma cutting of a branch pipe with a single Y-groove.Firstly,it summarizes the intersection forms and introduces a dual-pipe intersection model.Based on this model,the moving three-plane structure(a description unit of the geometric characteristics of the intersecting curve)is constructed,and a geometric model of the branch pipe with a single Y-groove is defined.Secondly,a novel mathematical model for plasma radius and taper compensation is established.Then,the compensation model and groove model are integrated by establishing movable frames.Thirdly,to prevent collisions between the plasma torch and workpiece,the torch height is planned and a branch pipe-rotating scheme is proposed.Through the established models and moving frames,the planned path description of cutting robot is provided in this novel scheme.The accuracy of the proposed method is verified by simulations and robotic cutting experiments.展开更多
Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ ...Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ j≤n, aj≥p}, Sp(r)={sp(a) |aam}, and WP(A)=P(si-p).Fis called an I-intersecting family if, for any a,6eF, a.Abi=min(ai,6i)>p for at least t i'8. F iscalled a greedy Ir-illtersecting flaily if F is an Ir-intersecting family and WP(A)ZWr(B+A') forany ASp and any BOA with B=t-1.In this paper, we obtain a sharp upper bound of for greedy Ir-intersecting families inM(sl,s2Z,'',sn.) for the case 2p5B' (IBIds) and 81 >BZ >...>B..展开更多
Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalitie...Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalities for non-empty cross-2-intersecting families of a- and i- subsets are obtained for some n and b . A new proof for a Frankl-Tokushige theorem [6] is also given.展开更多
We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Th...We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.展开更多
This paper focuses on the simulation analysis of stripe formation and dynamic features of intersecting pedestrian flows.The intersecting flows consist of two streams of pedestrians and each pedestrian stream has a des...This paper focuses on the simulation analysis of stripe formation and dynamic features of intersecting pedestrian flows.The intersecting flows consist of two streams of pedestrians and each pedestrian stream has a desired walking direction.The model adopted in the simulations is the social force model, which can reproduce the self-organization phenomena successfully. Three scenarios of different cross angles are established. The simulations confirm the empirical observations that there is a stripe formation when two streams of pedestrians intersect and the direction of the stripes is perpendicular to the sum of the directional vectors of the two streams. It can be concluded from the numerical simulation results that smaller cross angle results in higher mean speed and lower level of speed fluctuation. Moreover, the detailed pictures of pedestrians＇ moving behavior at intersections are given as well.展开更多
基金supported by National Nautural Science Foundation of China(Grant No.50775002)Key Science and Technology Research Program of Beijing Municipal Commission of Education of China(Grant No.KZ200910005003)
文摘All-position robots are widely applied in the welding of complicated parts.Welding of intersecting pipes is one of the most typical tasks.The welding seam is a complicated saddle-like space curve,which puts a great challenge to the pose planning of end-effector.The special robots designed specifically for this kind of tasks are rare in China and lack sufficient theoretical research.In this paper,a systematic research on the pose planning for the end-effectors of robot in the welding of intersecting pipes is conducted. First,the intersecting curve of pipes is mathematically analyzed.The mathematical model of the most general intersecting curve of pipes is derived,and several special forms of this model in degraded situations are also discussed.A new pose planning approach of bisecting angle in main normal plane（BAMNP） for the welding-gun is proposed by using differential geometry and the comparison with the traditional bisecting angle in axial rotation plane（BAARP） method is also analytically conducted.The optimal pose of the welding-gun is to make the orientation posed at the center of the small space formed by the two cylinders and the intersecting curve to help the welding-pool run smoothly.The BAMNP method can make sure the pose vertical to the curve and center between the two cylinders at the same time,therefore its performance in welding-technique is superior to the BAARP method.By using the traditional BAARP method,the robot structure can become simpler and easier to be controlled,because one degree of freedom（DOF） of the robot can be reduced.For the special case of perpendicular intersecting,an index is constructed to evaluate the quality of welding technique in the process of welding.The effect of different combination of pipe size on this index is also discussed.On the basis of practical consideration,selection principle for BAARP and BAMNP is described.The simulations of those two methods for a serial joint-type robot are made in MATLAB,and the simulation results are consistent to the analys
文摘The stress analysis based on the theory of a thin shell is carried out for cylindrical shells with normally intersecting nozzles subjected to external moment loads on the ends of shells with a large diameter ratio(ρ 0 ?0. 8). Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable toρ 0(R/T)1/2 ?1, is used for the analysis of the shell with cutout. The solution in terms of displacement function for the nozzle with a nonplanar end is based on the Goldenveizer equation. The boundary forces and displacements at the intersection are all transformed from Gaussian coordinates (α, β) on the shell, or Gaussian coordinates (ζ, θ) on the nozzle into three-di-mensional cylindrical coordinates(ρ,θ, z). Their expressions on the intersecting curve are periodic functions ofθ and expanded in Fourier series. Every harmonic of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature. The results obtained are in agreement with those from the three-dimensional finite element method and experiments.
基金supported by National Natural Science Foundation of China (Grant No. 11701407)
文摘Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.
基金the National Natural Science Foundation of China(Grant No.62103234)the Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021QF027,ZR2022QF031).
文摘The automatic cutting of intersecting pipes is a challenging task in manufacturing.For improved automation and accuracy,this paper proposes a model-driven path planning approach for the robotic plasma cutting of a branch pipe with a single Y-groove.Firstly,it summarizes the intersection forms and introduces a dual-pipe intersection model.Based on this model,the moving three-plane structure(a description unit of the geometric characteristics of the intersecting curve)is constructed,and a geometric model of the branch pipe with a single Y-groove is defined.Secondly,a novel mathematical model for plasma radius and taper compensation is established.Then,the compensation model and groove model are integrated by establishing movable frames.Thirdly,to prevent collisions between the plasma torch and workpiece,the torch height is planned and a branch pipe-rotating scheme is proposed.Through the established models and moving frames,the planned path description of cutting robot is provided in this novel scheme.The accuracy of the proposed method is verified by simulations and robotic cutting experiments.
文摘Let n, s1,s2, and sn be positive integers. Assume M(s1 s2,,sn)={(x1,x2,... ,xn)|0≤xi≤si, xi is an integer for each i}.For a=(a1,a2,....,an)∈M(s1,s2,...,sn.),M(s1,s2,....,sn.), and A{1,2,..,n}, denote sp(a)={j |1≤ j≤n, aj≥p}, Sp(r)={sp(a) |aam}, and WP(A)=P(si-p).Fis called an I-intersecting family if, for any a,6eF, a.Abi=min(ai,6i)>p for at least t i'8. F iscalled a greedy Ir-illtersecting flaily if F is an Ir-intersecting family and WP(A)ZWr(B+A') forany ASp and any BOA with B=t-1.In this paper, we obtain a sharp upper bound of for greedy Ir-intersecting families inM(sl,s2Z,'',sn.) for the case 2p5B' (IBIds) and 81 >BZ >...>B..
基金Suppored by Postdoctral Fellowship Foundation of China
文摘Let Cnk denote the set of all t -subsets of an n -set. Assume A ∈ Cnk and B∈Cn.b (A,B) is called a cross-2-intersecting family if |A∩B|≥2 for any A∈A, B∈B.In this paper, the best upper bounds of the cardinalities for non-empty cross-2-intersecting families of a- and i- subsets are obtained for some n and b . A new proof for a Frankl-Tokushige theorem [6] is also given.
文摘We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.
基金Project supported by the National Natural Science Foundation of China(Grant No.61233001)the Fundamental Research Funds for the Central Universities,China(Grant No.2017JBM014)
文摘This paper focuses on the simulation analysis of stripe formation and dynamic features of intersecting pedestrian flows.The intersecting flows consist of two streams of pedestrians and each pedestrian stream has a desired walking direction.The model adopted in the simulations is the social force model, which can reproduce the self-organization phenomena successfully. Three scenarios of different cross angles are established. The simulations confirm the empirical observations that there is a stripe formation when two streams of pedestrians intersect and the direction of the stripes is perpendicular to the sum of the directional vectors of the two streams. It can be concluded from the numerical simulation results that smaller cross angle results in higher mean speed and lower level of speed fluctuation. Moreover, the detailed pictures of pedestrians＇ moving behavior at intersections are given as well.
