Potential Energy Surfaces for Conceptual Design and Analysis of Mechanical Systems

Current computational Design Synthesis approaches have had trouble generating components with higher kinematic pairs and have instead relied on libraries of predefined components. However, higher kinematic pairs are ubiquitous in many mechanical devices such as ratchets, latches, locks, trigger mechanisms, clock escapements, and materials handling systems. In many cases there is a need to synthesize new higher kinematic pair devices. To address this problem, we develop a new representation for mechanical systems that extends the capabilities of configuration spaces to consider arbitrary energy storing mechanical devices. The key idea underlying this representation is the use of potential energy surfaces as a generalization of configuration spaces. This generalization enables modelling of mechanical systems in a physics independent manner and captures behaviors such as dynamics. By modeling a device through the lens of a potential energy surface, we demonstrate that differentiable simulation is possible. Differentiable simulation enables efficient calculation of gradients of potential energy surface parameters with respect to an objective function that depends on trajectories taken on the potential energy surface. This allows synthesis of mechanical devices with desired kinematic and dynamic behavior through gradient descent. We demonstrate this through several synthesis examples including positioning devices (e.g., a funnel) and timing devices (e.g., an oscillator).

Structural Synthesis of Lower-Class Robot Manipulators with General Constraint One

In this research, the structural synthesis of lower-class robot manipulators with general constraint one is investigated. The number of constraints d = 1 and the mobility number λ = 5 for sphere–sphere and sphere–plane combinations of higher kinematic pairs are investigated by using the analytical approach. Structural synthesis of new first- and second-class robot manipulators is investigated by using transformations of higher kinematic pairs to lower kinematic pairs. Therefore, using this approach, we obtain structural groups with general constraint one. Further, kinematic structures and physical models of overconstrained robot manipulators are presented in the research.

Replacement in a Plane Geared Linkage of High Kinematic Pairs with Lower Pairs

The analysis of constraints in plane mechanisms is an urgent problem in the theory of machines and mechanisms. Although kinematic pairs’ classification has been known for a long time, the issue of the conjugation of links, being at the heart of the analysis and synthesis of mechanisms and machines, is of considerable theoretical and practical interest and continues to attract scientists. One of the tasks that are solved in the process of analysis and synthesis of the structures of mechanisms is the re-placement of higher kinematic pairs by lower ones. As a rule, such a replacement is made to identify kinematic chains of zero mobility, Assur's structural groups, in a mechanism. The replacement may also aim at obtaining the necessary kinematic relations. That is because specific computational difficulties hamper the kinematic analysis of chains with higher kinematic pairs due to the relative sliding and shape irregularity of mating surfaces. Yet, the use of replacements to obtain kinematic and transmission functions is difficult due to nonisomorphism of the equivalent mechanism. Simultaneously, for mixed-type mechanisms, which include geared linkages, the equivalent replacement will allow unifying the kinematic analysis methods. The paper suggests the technology of replacing higher kinematic pairs with links with lower pairs as applied to a plane geared linkage. The technology is based on the properties of the involute of a circumference. The paper proved the structural and kinematic equivalence of such a replacement. The isomorphism of the equivalent linkage will enhance the kinematic analysis, make it possible using kinematic functions, and applying methods based on the instantaneous relative rotations of links, in particular, the Aronhold-Kennedy theorem. Another application of the replacement method presented in the paper will be the expansion of opportunities for identifying idle constraints in the mechanism.

Epoxy toughening through high pressure and shear rate preprocessing

We have successfully conceived and demonstrated a simple, scalable process for improving the fracture energy of epoxy resins. The process is based on the combined application of high pressures (in the order of GPa) and shear rates (in the order of 106 s−1) in the pre-cured polymer, obtaining mechanical forces sufficiently high to increase the reactivity of the monomers due to the scission of the epoxy groups. To achieve these high values of pressure and shear rate, we take advantage of the elastohydrodynamic phenomena occurring at lubricated higher kinematic pairs as, for example, the rolling element – track pair in ball bearings. Experimental results show that, under certain combinations of pressure and shear rate, a substantial improvement in fracture toughness is obtained. SEM observations, Raman spectroscopies, nanoindentation and GPC and NMR measurements show that the process is able to increase the polymer chain length before curing, reducing the number of potential anchor points during the subsequent curing and hence reducing the crosslinking density. The chain lengths obtained are big enough to guarantee adequate stiffness and strength due to increased chain tangling, hence overcoming the drawbacks associated with other toughness promotion methods, such as stiffness and strength reduction.

Computational Local Mobility Analysis of Mechanisms With Higher Kinematic Pairs

The finite mobility of a mechanism is reflected by its configuration space (c-space), and the mobility analysis aims at determining this c-space. Crucial for the computational mobility analysis is an adequate formulation of the constraints. For lower pair linkages an analytic formulation is the product-of-exponential (POE) formula in terms of the screw systems of the lower pair joints. In other words, the screw coordinates of a lower pair joint serve as canonical coordinates on the corresponding motion subgroup. For such linkages, a computational approach to the local mobility analysis has been reported recently. The approach is applicable to general multi-loop linkages. Higher pairs do not generate motion subgroups so that their motion cannot be expressed in terms of screw coordinates. Hence their kinematics cannot be expressed in terms of a POE, and there is no efficient and generally applicable computational method for the mobility analysis. In this paper a formulation of higher-order constraints for mechanisms with higher pair joints is proposed making use of the result for lower pair linkages. The method is applicable to mechanisms where each fundamental loop comprises no more than one higher pair, which covers the majority of mechanisms. Based on this, a computational algorithm is introduced that allows mobility determination. As for lower pair linkages, this algorithm only requires simple algebraic operations.