.... A variable is defined to combine the time set with the displacement set. Boolean algebraic theorems are extended to derive a compact expression for the contact graph that supports the organization of accumulations at different surfaces with propagations through physical domains. Demonstrations of this method...

... are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-R P R PPMs with regard to their dexterity, workspace size...

... reduction for simulation. This is highly efficient for large deformation analysis, but contact detection can pose challenges. Moreover, for complex snap-fits, extracting cross-sectional properties for 1D formulation is nontrivial. We propose here a nonlinear algebraic dimensional reduction method...

... beams, buckling beams, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method...

... structural analysis and mechanism solution programs. Joint reaction forces, torques, speeds, and power consumptions are also checked. Algebraic equations of this new spherical CV coupling mechanism are derived. This mechanism has the advantage of a very compact structure and uses only standard radial...

...Yi Zhang; Kwun-Lon Ting This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description...

...Giorgio Figliolini; Jorge Angeles The synthesis of the pitch surfaces of any pair of external and internal skew gears, using dual algebra and the principle of transference, is the subject of this paper. The spatial motion of the Euclidean space is transferred to the dual space in order to obtain...

...Erika Ottaviano; Manfred Husty; Marco Ceccarelli In this paper an algebraic formulation is presented for the boundary workspace of 3-R manipulators in Cartesian Space. It is shown that the cross-section boundary curve can be described by a 16th order polynomial as function of radial and axial...

... of the Lie algebra, s e (3), also known as screw algebra, of the Euclidean group, S E (3). Moreover, it should be emphasized that, unlike other attempts to develop a criterion, the criterion developed in this contribution does not require any consideration of reciprocal screws. As is common in many areas...

...Kwun-Lon Ting, Professor; Yi Zhang, Research Assistant The article presents a unified algebraic approach for the modeling of the instantaneous motions of all linear elements, such as points, lines, and planes, embedded in a rigid body. The paper first addresses the Clifford algebra based...

...Glen Mullineux This paper looks at the use of a Clifford (or geometric) algebra for handling both rotations and translations in Euclidean space. The algebra is constructed over the real numbers using four basis vectors. Three of these generate a subalgebra which models three-dimensional space...

... and the given screw system easily. With the results, to find a reciprocal screw is to solve an algebraic equation of the corresponding system of screws. In order to show the usefulness of the result, several examples related to the robot manipulator are provided. For a nonredundant serial manipulator...

... are generally expressed in terms of Differential-Algebraic Equations (DAEs). Conventional methods of linearization are based on the perturbation of the nonlinear DAE, where small amounts of perturbations are taken to guarantee linear characteristics of the equations. On the other hand, the proposed linearized...

...Shih-Tin Lin, Professor; Jiann-Nan Huang, Graduate Research Assistant The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAE). The DAE systems cannot be solved using numerical integration methods that are commonly used...