... number of links, type of joint, and number of joints needed to achieve a given number of degrees of freedom of a desired mechanism. During this phase of study, the designermakes sure that a mechanism ... phases of the design processwere introduced. Then, a systematic design methodology for the enumeration of kinematicstructuresof mechanisms was outlined. Fundamental terminologies formechanisms ... requirements, of aclass of mechanisms of interest.2. Determine the nature of motion (i.e., planar, spherical, or spatial mechanism) ,degrees of freedom (dof), type, and complexity of the mechanisms.3....
... Au-tomatic Generation of the KinematicStructuresof Mechanism, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 108, 3, 392–398.[5] Woo, L.S., 1967, Type Synthesis of Plane Linkages, ... 2 to the sum of theproduct i × Li. Hence,iiLi= 2e. (2.7)Let vkdenote the number of vertices of degree k, namely,v2denotes the number of vertices of degree two, v3the number of ... number of independent loops of a planar connected graph and˜Lrepresent the total number of loops. Then˜L = L + 1 . (2.1)Euler’s equation, which relates to the number of vertices, the number of...
... perpendicular to each other with an offsetdistance. Both mechanisms are capable of converting the rotational motion of link 2into the reciprocating and oscillatory motions of link 4. These two mechanisms ... Development of an Atlas of the Kinematic Structuresof Mechanisms, in Proceedings of the ASME MechanismsConference, Cambridge, MA, Paper No. 84-DET-21.[10] Sohn, W., 1987, A Computer-Aided Approach to ... useful for computer aided enumerationof kinematic structuresof mechanisms. In the following, we briefly describe the adjacency andincidence matrix representations ofkinematic chains.3.5.1 Adjacency...
... Isomorphic mechanisms4.3 Degrees of FreedomThe degrees of freedom of a mechanism is perhaps the first concern in the study of kinematics and dynamics of mechanisms. The degrees of freedom of a mechanism refers ... degrees of freedom of the space in which a mechanism is intended to function. It is assumed that a single value of λ applies to the motion of all the links of a mechanism. For spatial mechanisms, λ ... 4.1Correspondence Between Mechanisms and Graphs.Graph Symbol Mechanism SymbolNumber of verticesvNumber of linksnNumber of edgeseNumber of jointsjNumber of vertices of degreeiviNumber of links havingijointsniDegree...
... number of gear pairs is equal to the number of independentloops; the number of turning pairs is equal to the number of links diminished by one;and the number of degrees of freedom is equal to the ... graph of n vertices. However, some of the graphs may be rejected due to violation of the structural characteristics, whereasothers may be isomorphic to one another. Hence, the total number of nonisomorphicunlabeled ... approach has been successfully employed for the enumerationof one-dof EGTswith up to five independent loops [9, 14], and the enumerationof two-dof EGTs [16].7.5 Parent Bar Linkage MethodIn...
... manipulators for which the number of limbsis equal to the number of degrees of freedom of the manipulator, and the total number of joint degrees of freedom in each limb is equal to the value of Ck.The ... Japan.) kinematic structuresof parallel manipulators accordingto their nature of motion anddegrees of freedom.9.2.3 Enumerationof Planar Parallel ManipulatorsFor planar manipulators, λ = 3. Furthermore, ... spherical, and spa-tial mechanisms. The kinematicstructuresof parallel manipulators are enumerated according to their degrees of freedom and connectivity listing [22].9.2.1 Functional RequirementsAs...
... accomplished by a com-puter program using a nested-do loops algorithm to vary the value of each xiandcheck for the validity of the solutions. A more rigorous procedure for solving onelinear ... first discuss a method for solving one equation in n unknowns. Then, we extendthe method to solving a system of m equations in n unknowns.A.1 Solving One Equation in n UnknownsConsider the following ... coefficients. The cis are nonnegativeintegers and k is a positive integer. We wish to solve for xi, for i = 1, 2, ,nsubject to a constraint that all xis must be nonnegative integers. In addition,...