In this paper, a simple single variable shear deformable nonlocal theory for bending of micro- and nano-scale rectangular beams is presented. To incorporate small size effects, the theory uses Eringen’s nonlocal differential constitutive relations. The theory has only one fourth-order governing differential equation involving a single unknown variable. The governing equation and the expressions for the bending moment and shear force of the present theory are strikingly similar to those of nonlocal Euler-Bernoulli Beam Theory (EBT) formulatedbased on Eringen’s nonlocal elasticity theory. The theory assumes that the axial and lateral displacements have bending and shear components such that the bending components do not contribute towards shear force, and theshear components do not contribute towards bending moment. Also, the chosen displacement functions of the theory give rise to a realistic parabolic transverse shear stress distribution across the beam cross-section. Efficacy of the proposed theory is demonstrated through bending of simply supported, cantilever and clamped-clamped micro- and nano-scale beams of rectangular cross-section. The numerical results obtained by using the present are compared with those predicted by other nonlocal first-order and higher-order shear deformation beamtheories. The results obtained are quite accurate.

Simulation and study of joint clearances has usually focused on appropriate simulation strategies and their validation against experiments. The effect of joint clearances on the output of a mechanism has been usually evaluated qualitatively. The relative importance of different joints in a mechanism in producing deviation from the output of an ideal mechanism has not been studied. This work identifies the appropriate statistical measure for quantifying this deviation and uses it to rank the joints of one degree of freedom multi-loop planar mechanisms. The inversions of six-bar mechanism have been studied through ADAMS simulations involving different clearance sizes and speed of crank. A trend in clearance location ranking has been identified which canprobably be extended to planar mechanisms of higher complexity.