TL;DR: In this article, the tables and equations of the first paper of this series are adapted to this more general class of molecules and additional approximations are involved and these are examined carefully.
Abstract: Formulas are derived which make the tables and equations of the first paper of this series applicable to this more general class molecules Additional approximations are involved and these are examined carefully
TL;DR: A force sensing touchpad as discussed by the authors comprises a substantially rigid touch surface, a substantial rigid frame, a plurality of spring structures formed integrally with the touch surface and mechanically connected to the reference frame, and a circuit for deriving force information.
Abstract: A force sensing touchpad comprises a substantially rigid touch surface; a substantially rigid frame; a plurality of spring structures formed integrally with the touch surface and mechanically connected to the reference frame; and a circuit for deriving force information from capacitances proportional to the distances between predetermined portions of the touch surface and portions of the frame in response to a force applied to the touch surfaces.
TL;DR: It is shown that a multi-graph can be realized as a rigid linkage of rigid bodies in n-space if and only if it contains n(n + 1)2 edge disjoint spanning trees.
TL;DR: In this paper, the relationship between forces and displacements at the ends of a member with elastically restrained ends is derived in matrix form and the force components, in terms of the end displacements, are arranged in a matrix form.
Abstract: Frames with semi-rigid connections are investigated. Relationships between forces and displacements at the ends of a member with elastically restrained ends are derived. The force components, in terms of the end displacements, are arranged in matrix form. Stiffness matrices of a member with elastic restraint at the ends are presented, in the form of the stiffness matrices for members with rigid connections, modified by a correction matrix whose elements are functions of parameters, designated as fixity factors of the member. A formula for the force components at the ends of all the members of a frame is established. The matrix operations involved are conveniently performed by any digital computer, and problems ranging from rigid frames to pin-connected trusses can be solved by the same systematic approach. Several numerical examples are solved.