Characteristics of the double-cycled motion-ruled surface of the Schatz linkage based on differential geometry

This paper applies Euclidean invariants from differential geometry to kinematic properties of the ruled surfaces generated by the coupler link and the constraint-screw axes. Starting from investigating the assembly configuration, the work reveals two cycle phases of the coupler link when the input link finishes a full rotation. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link, where Euclidean invariants are obtained and singularities are identified. This work further presents the constraint ruled surface that is generated by the constraint screw axes and unveils its intrinsic characteristics

Alternating Error Effects on Decomposition Method in Function Generation Synthesis

In approximate function generation synthesis methods, error between the desired function’s output and designed mechanism’s output oscillate about zero error while crossing the zero error margin at precision points. The common goal of these methods is to minimize the error within the selected working region of the mechanism. For mechanisms like Bennett overconstrained six-revolute jointed linkages that have relatively large number of construction parameters, it is a difficult task to solve for them at once. Decomposition method enables to divide such linkages into two loops and independently solve for each loop with less construction parameters. Although some approximation methods are proven to produce smaller errors than others for a single-loop synthesis, in this work, it is shown that smaller errors are not guaranteed for a certain method when used along with decomposition method. Numerical examples indicate that in decomposition method, more attention should be given to the alternation of the error of each decomposed mechanism, rather than the approximation method used

Reconfigurable chains of bifurcating type III Bricard linkages

This paper presents the construction of a family of reconfigurable mechanisms composed of an unlimited number of doubly collapsible (type III) Bricard linkages. First, the geometries of these overconstrained six-hinge spatial loops are parameterized and their kinematics is investigated. The configurationspace curve is computed; its bifurcation behavior is analyzed and illustrated by projections. It is then shown that type III Bricard linkages can be connected in series in a one-degree-of-freedom chain. Such a multi-loop mechanism has the ability to reconfigure in multiple ways due to the bifurcations of the individual Bricard units. Consequently, the chain has multiple states where all joint axes are coplanar. In each such configuration, the physical links, every one realized as a planar figure, spread out to cover a curving stripe in the plane. Several simulations and case studies are performed