Novel Mobility Formula for Parallel Mechanisms Expressed with Mobility of General Link Group

The determination of virtual constraints is always one of the key and difficult problems in traditional mobility calculation. To make mobility calculation simple, considering avoiding virtual constraints, some new formulae have been presented, however these formulae can hardly intuitively reflect general link group＇s restrictions on output member and its influences on independence of output parameters, which is premise to the judgment of the properties of mobility. Towards the problem to reveal the intrinsic relationship between the degree of freedom（DOF） of a mechanism, the link group, and the dimension of output parameters, also to avoid determination of virtual constraint, based on the new concepts of the ＂DOF of general link group＂ and ＂node parameters＂, a new formula in the calculation of the mobility of mechanisms is presented that is expressed with DOFs of the general link groups and rank of motion parameters of base point of the output link. It is named GOM（mobility of groups and output parameter） formula. On the basis of new concepts of＂effective parameters＂ and ＂invalid parameters＂, a rule is put forward for solving the DOF of mechanisms with invalid parameters by GOM formula, that is, the base point parameters are the subset of effective parameters of link group. Thereafter, several examples are enumerated and the results coincide with the prototype data, which proves the validity of the proposed formula. Meanwhile, it is obtained that the necessary and sufficient condition for the judgment of output parameters independence is that each of the DOF of the link group is not less than zero. The proposed formula which is simple in calculation provides theoretical basis for the judgment of independence of output parameters and provides references for type synthesis of novel parallel mechanisms with independence requirements of their output parameters.

New SRLG-diverse path selection algorithm in survivable GMPLS networks

In conventional shared risk link group （SRLG）-diverse path selection （CSPS） algorithm in survivable GMPLS networks, SRLG is taken into account when selecting the backup paths, while the primary path selection method is the sarne as the algorithms without SRLG constraint. A problem of CSPS algorithm is that, after a primary path is selected, the success probability to select an SRLG-diverse backup path for it is low. If SRLG is taken into account when computing the primary path, then the probability to successfully select an SRLG-diverse backup path will be much increased. Based on this idea, an active SRLG-diverse path selection （ASPS） algorithm is proposed. To actively avoid selecting those SRLG links, when computing the primary path, a link that share risk with more links is assigned a larger link cost. To improve the resource utilization ratio, it is permitted that the bandwidth resources are shared among backup paths. What is more, differentiated reliability （DiR） requirements of different customers are considered in ASPS algorithm. The simulation results show that, compared with CSPS algorithm, ASPS algorithm not only increases successful protection probability but also improves resource utilization ratio.

The Symmetric Commutator Homology of Link Towers and Homotopy Groups of 3-Manifolds

A link tower is a sequence of links with the structure given by removing the last components.Given a link tower,we prove that there is a chain complex consisting of(non-abelian)groups given by the symmetric commutator subgroup of the normal closures in the link group of themeridians excluding themeridian of the last component with the differential induced by removing the last component.Moreover,the homology groups of these naturally constructed chain complexes are isomorphic to the homotopy groups of the manifold M under certain hypothesis.These chain complexes have canonical quotient abelian chain complexes in Minor’s homotopy link groups with their homologies detecting certain differences of the homotopy link groups in the towers.