... as link vectors of the linkage. By incorporating the loop closure equations and the kinematic constraints, the gravitational potential energy of the system can be formulated as the function of the vectors of all ground-adjacent links. The balance of the gravitational potential energy of the system...

...Pin Wang; Qizheng Liao; Yufeng Zhuang; Shimin Wei The position analysis of a nine-link Barranov truss is finished by using Dixon resultants together with Sylvester resultants. Above all, using vector method in complex plane to construct four constraint equations and transform them into complex...

...Ahmad Smaili; Nadim Diab A method for the synthesis of four-bar mechanisms to generate closed paths through shape optimization is herein introduced. The objective function is not based on Fourier descriptors, but rather on the cyclic angular deviation (CAD) vector associated with a set of desired...

... are obtained by intersecting two 3-systems corresponding to the finite displacements of the RP and PR dyads. The intersection of finite screw systems is conducted by employing the intersection operation of vector subspaces of the six-dimensional vector space. 06 01 2005 08 07 2005 couplings...

... on the location of its end-effector. On the other hand, a differential vector method is used to study the influence of the length and angular variations in the parts of the manipulator on the position and orientation of its end-effector. Besides, this method takes into account the variations in the parallelograms...

... of striction as the intersection of two comparatively simple surfaces. Because of its special significance in this case, we also obtain the equation to the central tangent surface. A feature of the investigation is the direct employment of screw vectors in dual format rather than unit line vectors...

.... A triad is a chain of three vectors connected tail-to-tip (see Fig. 5 ). The first vector in the chain (attached to ground) is W , the middle vector is V , and the final vector is Z . The angular positions of these vectors at the design positions are α i , β i , and γ...

... of the wrench system. Let [ 0 i ] , [ 0 j ] , and [ 0 k ] denote a base of W and [ ζ Sj _ i ζ Fj _ i ] represents ζ j _ i . Here, i , j , and k denote, respectively, the unit vectors...

... of S ^ can be obtained as u = r S 2 − r S 1 e ^ S sin   γ = n ^ 1 × n ^ 2 e ^ S where r S 1 and r S 2 denote the position vectors of R S 1 and R S 2...