A New Matrix Method for the Kinematic Analysis and Motion Simulation of Planar Mechanisms With Lower Pairs

This paper presents a new matrix method for the kinematic analysis and the determination of the velocities, accelerations and jerks for planar mechanisms incorporating rolling, sliding, and pivoting members with a single or multiple degrees of freedom. It also presents a motion simulation procedure that uses the results of the kinematic analysis to estimate the successive positions of the members during the cycle of operation of the mechanism, with third order accuracy in time. Due to the improved accuracy, the proposed motion simulation procedure presents minimal member distortion caused by the accumulation of numerical errors, and does not require iterations for its convergence.

More about uniform upper bounds on ideals of turing degrees

Let I be a countable jump ideal in = 〈The Turing degrees, ≤〉. The central theorem of this paper is:a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a(1) computes.We may replace “the join of an I-exact pair” in the above theorem by “a weak uniform upper bound on I”.We also answer two minimality questions: the class of uniform upper bounds on I never has a minimal member; if ⋃I = Lα[A] ⋂ ωω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds.The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces.

Semigroups satisfying minimal conditions

In his fundamental paper, “On the structure of semigroups” [6], J. A. Green has examined certain important minimal conditions which may be satisfied bya semigroup S.We say that S satisfies the minimal condition on principal left ideals if every set of principal left ideals of S contains a minimal member with respect to inclusion:this condition is denoted by ℳ1. The corresponding conditions on principal rightideals and principal two-sided ideals are denoted by ℳr and ℳ1 respectively. The purpose of the present paper is to give some further results concerning these three conditions.Extensive use is made of the work of A. H. Clifford ([3] and [4]) onminimal ideals.