Configuration analysis of complex multiloop linkages and manipulators

Polynomial Solution to the Position Analysis of Two Assur Kinematic Chains With Four Loops and the Same Topology

“…. ,4; k = ͑i +1͒ modulo 4͒: 5 The measure of the convex central angle between two radius vectors gives the distance, on the unit sphere, between the two points located on the sphere by the two radius vectors. …”

Position analysis of Assur kinematic chains using coupler curves

“…If the curve has full circularity, then i min ¼ 0, O ¼ 2k, and C ¼ k. By taking the planar four-bar linkage with all joints being revolute as an example, the coupler curve equation has order 6 and circularity 3 and is then expressed as [6,3]. The maximum number of solutions is discussed on the basis of the characteristics of two coupler curve equations.…”

“…If the linkage with point B 0 being a prismatic joint is considered, the coupler point curve is [10,3]. Moreover, the coupler point curve is [6,1] if both points A 0 and B 0 are prismatic joints. The characteristics of these four coupler curve equations are all listed in Table 1.…”

“…Two other seven-link AKCs with all revolute joints were analysed by solving several loop equations to obtain 18 and 14 solutions [4,5]. For the nine-link AKC, 28 types were listed in reference [6]. However, only two of them have been investigated to obtain 48 and 54 solutions [7,8].…”

Synthesis and structure analysis of kinematic structures of 6-dof parallel robotic mechanisms

“…limb), and p denotes the ''platform''So far, taking into account the seven basic design requirements given in Section 1, we obtain 29 wanted parallel structures listed in Table 2, but this by no means covers every possible 6-dof parallel structures [15]. The reader can quite easily obtain other combination arrangements of limb configurations and sketch out the corresponding structures.…”