It is well known that singular configurations are an inherent nature of mechanical systems and have important influences on their properties. Therefore, these special configurations of the system are usually avoided in design and application of mechanisms. For simple 2-DOF and 3-DOF planar manipulators, the singularity loci have been obtained in [1, 2]. For spherical 3DOF parallel manipulators ...

The x-intersection graphs are the graphs that have a representation as intersection graphs of axis parallel x shapes in the plane. A subfamily of these graphs are {x, |,−}-contact graphs which are the contact graphs of axis parallel x, |, and − shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt in 2013. We show that planar graphs are x-intersection gra...

A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three legged, three degree of freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The invers...

In Long-Evans rats the area of the cerebellum was irradiated with multiple doses of low-level X-ray beginning on day 12 after the bulk of stellate cells were acquired. The treatment spared basket, stellate and early-forming granule cells but led to a substantial reduction in the total granule cell population and a correlated miniaturization of the cerebellar cortex. Nevertheless most Purkinje c...