Harmonic drive gears are widely used in space applications, robotics, and precision positioning systems because of their attractive attributes including near-zero backlash, high speed reduction ratio, compact size, and small weight. On the other hand, they possess an inherent periodic positioning error known as kinematic error responsible for transmission performance degradation. No definite understanding of the mechanism of kinematic error as well as its characterization is available in the literature. In this paper, we report analytical and experimental results on kinematic error using a dedicated research Harmonic Drive Test Apparatus. We first show that the error referred to in the literature as kinematic error actually consists of a basic component, representing “pure” kinematic error, colored with a second component resulting from inherent torsional flexibility in the harmonic drive gear. The latter component explains the source of variability in published kinematic error profiles. The decomposition of the kinematic error into a basic component and a flexibility related component is demonstrated experimentally as well as analytically by matching a mathematical model to experimental data. We also characterize the dependence of the kinematic error on inertial load, gear assembly, and rotational speed. The results of this paper offer a new perspective in the understanding of the mechanism of kinematic error and will be valuable in the mechanical design of harmonic drive gears as well as in the dynamic modeling and precision control of harmonic drive systems.

Abstract-This paper presents a new approach to design a sliding mode controller for a class of mismatched uncertain systems. A method is proposed for the design of a switching surface in the presence of mismatched uncertainties. A design method for a sliding mode observer based on high gain is also proposed in this paper to reconstruct the states of the system for the implementation of sliding mode control. The design technique is simple and computationally efficient. A control problem for the slosh-free motion of a container is considered as the representative of a typical class of systems. A simple pendulum model is considered to represent the lateral slosh. The validity of the proposed scheme is demonstrated by simulation along with the experimental results.Index Terms-Sliding mode control (SMC), sliding mode observer (SMO), slosh.

In this paper, we propose a new dynamic model to describe the hysteresis phenomenon in harmonic drives. The experimental observation of the dynamic torque-displacement relationship for a harmonic drive shows a hysteresis characteristic indicating the simultaneous presence of energy storage and energy dissipation mechanisms. To completely characterize these mechanisms and yet have a simple representation for control, we develop a new hysteresis model using the heredity concept of dynamic systems. This model represents the hysteresis phenomenon by a combination of a nonlinear stiffness component and a nonlinear damping component leading to a mathematically well-posed nonlinear differential equation. The parameters of the model are identified using optimization techniques. We present some important mathematical properties of the model that give insight into model behavior and thus establish a mathematical basis for control. Numerical simulations in comparison with experimental data using our Harmonic Drive Test Apparatus verify the accuracy of the proposed model to represent the complex hysteresis dynamics of harmonic drives.

Flexible link systems are increasingly becoming popular for advantages like superior performance in micro/nanopositioning, less weight, compact design, lower power requirements, and so on. The dynamics of distributed and lumped parameter flexible link systems, especially those in vertical planes are difficult to capture with ordinary differential equations (ODEs) and pose a challenge to control. A representative case, an inverted flexible pendulum with tip mass on a cart system, is considered in this paper. A dynamic model for this system from a control perspective is developed using an Euler Lagrange formulation. The major difference between the proposed method and several previous attempts is the use of length constraint, large deformations, and tip mass considered together. The proposed dynamic equations are demonstrated to display an odd number of multiple equilibria based on nondimensional quantity dependent on tip mass. Furthermore, the equilibrium solutions thus obtained are shown to compare fairly with static solutions obtained using elastica theory. The system is demonstrated to exhibit chaotic behavior similar to that previously observed for vibrating elastic beam without tip mass. Finally, the dynamic model is validated with experimental data for a couple of cases of beam excitation.

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The pursuit of mimicking complex multiscale systems has been a tireless effort with many successes but a daunting task ahead. A new perspective to engineer complex cross-linked meshes and branched/tree-like structures at different scales is presented here. Control over Saffman-Taylor instability which otherwise randomly rearranges viscous fluid in a ‘lifted Hele-Shaw cell’ is proposed for the same. The proposed control employs multiple-ports or source-holes in this cell, to spontaneously shape a stretched fluid film into a network of well defined webs/meshes and ordered multiscale tree-like patterns. Use of multiple ports enables exercising strong control to fabricate such structures, in a robust and repeated fashion, which otherwise are completely non-characteristic to viscous fingering process. The proposed technique is capable of fabricating spontaneously families of wide variety of structures over micro and very large scale in a period of few seconds. Thus the proposed method forms a solid foundation to new pathways for engineering multiscale structures for several scientific applications including efficient gas exchange, heat transport, tissue engineering, organ-on-chip, and so on. Proposal of multi-port Hele-Shaw cell also opens new avenues for investigation of complex multiple finger interactions resulting in interesting fluid patterns.

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