Walking robots use leg structures to overcome obstacles or move on complicated terrains. Most robots of current researches are equipped with legs of simple structure. The specific design method of walking robot legs i...Walking robots use leg structures to overcome obstacles or move on complicated terrains. Most robots of current researches are equipped with legs of simple structure. The specific design method of walking robot legs is seldom studied. Based on the generalized-function(GF) set theory, a systematic type synthesis process of designing robot legs is introduced. The specific mobility of robot legs is analyzed to obtain two main leg types as the goal of design.Number synthesis problem is decomposed into two stages, actuation and constraint synthesis by name,corresponding to the combinatorics results of linear Diophantine equations. Additional restrictions are discussed to narrow the search range to propose practical limb expressions and kinematic-pair designs. Finally, all the fifty-one leg structures of four subtypes are carried out, some of which are chosen to make up robot prototypes, demonstrating the validity of the method. This paper proposed a novel type synthesis methodology, which could be used to systematically design various practical robot legs and the derived robots.展开更多
Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. ...Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.展开更多
In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts ...In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.U1613208,51335007)National Basic Research Program of China(973 Program,Grant No.2013CB035501)+1 种基金Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51421092)Science and Technology Commission of Shanghai-based "Innovation Action Plan" Project(Grant No.16DZ1201001)
文摘Walking robots use leg structures to overcome obstacles or move on complicated terrains. Most robots of current researches are equipped with legs of simple structure. The specific design method of walking robot legs is seldom studied. Based on the generalized-function(GF) set theory, a systematic type synthesis process of designing robot legs is introduced. The specific mobility of robot legs is analyzed to obtain two main leg types as the goal of design.Number synthesis problem is decomposed into two stages, actuation and constraint synthesis by name,corresponding to the combinatorics results of linear Diophantine equations. Additional restrictions are discussed to narrow the search range to propose practical limb expressions and kinematic-pair designs. Finally, all the fifty-one leg structures of four subtypes are carried out, some of which are chosen to make up robot prototypes, demonstrating the validity of the method. This paper proposed a novel type synthesis methodology, which could be used to systematically design various practical robot legs and the derived robots.
基金supported by Grants-in-Aid for Scientific Research(JSPS KAKENHI) (Grant No. 16K05079)
文摘Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10401021)
文摘In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s + 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax + by = n which is given by Popoviciu in 1953.
