Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

Geometry Based Synthesis of Planar Compliances with Redundant Mechanisms Having Five Compliant Components

In this paper, a geometric approach to the passive realization of any planar compliance with a redundant compliant mechanism is presented. The mechanisms considered are either simple serial mechanisms consisting of five elastic joints or simple parallel mechanisms consisting of five springs. For each type of mechanism, realization conditions to achieve a given compliance are derived. The physical significance of each condition is identified and graphically interpreted. Geometry based synthesis procedures to achieve any given compliance are developed for both types of mechanisms. Since each realization condition imposes restrictions solely on the mechanism geometry, the procedures allow one to choose the geometric properties of each component (from a set of admissible options) independently from the selection of the elastic properties of each component

Nonaffine rubber elasticity for stiff polymer networks

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (``stretching''). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of ``floppy modes'' -- low-energy bending excitations that retain a high degree of non-affinity. The length-scale characterizing the emergent non-affinity is given by the ``fiber length'' $l_f$, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.Comment: 12 pages, 10 figures, revised Section II

A Lumped-Mass Model for Large Deformation Continuum Surfaces Actuated by Continuum Robotic Arms

Currently, flexible surfaces enabled to be actuated by robotic arms are experiencing high interest and demand for robotic applications in various areas such as healthcare, automotive , aerospace, and manufacturing. However, their design and control thus far has largely been based on "trial and error" methods requiring multiple trials and/or high levels of user specialization. Robust methods to realize flexible surfaces with the ability to deform into large curvatures therefore require a reliable, validated model that takes into account many physical and mechanical properties including elasticity, material characteristics, gravity, external forces, and thickness shear effects. The derivation of such a model would then enable the further development of predictive-based control methods for flexible robotic surfaces. This paper presents a lumped-mass model for flexible surfaces undergoing large deformation due to actuation by continuum robotic arms. The resulting model includes mechanical and physical properties for both the surface and actuation elements to predict deformation in multiple curvature directions and actuation configurations. The model is validated against an experimental system where measured displacements between the experimental and modeling results showed considerable agreement with a mean error magnitude of about 1% of the length of the surface at the final deformed shapes

Topological analysis of a novel compact omnidirectional three-legged robot with parallel hip structures regarding locomotion capability and load distribution

In this study, a novel design for a compact, lightweight, agile, omnidirectional three-legged robot involving legs with four degrees of freedom, utilizing an spherical parallel mechanism with an additional non-redundant central support joint for the robot hip structure is proposed. The general design and conceptual ideas for the robot are presented, targeting a close match of the well-known SLIP-model. CAD models, 3d-printed prototypes, and proof-of-concept multi-body simulations are shown, investigating the feasibility to employ a geometrically dense spherical parallel manipulator with completely spherically shaped shell-type parts for the highly force-loaded application in the legged robot hip mechanism. Furthermore, in this study, an analytic expression is derived, yielding the calculation of stress forces acting inside the linkage structures, by directly constructing the manipulator hip Jacobian inside the force domain

Adaptive deformable mirror : based on electromagnetic actuators

Refractive index variations in the earth's atmosphere cause wavefront aberrations and limit thereby the resolution in ground-based telescopes. With Adaptive Optics (AO) the temporally and spatially varying wavefront distortions can be corrected in real time. Most implementations in a ground based telescope include a WaveFront Sensor, a Deformable Mirror and a real time wavefront control system. The largest optical telescopes built today have a ~ 1 Om primary mirror. Telescopes with more collecting area and higher resolution are desired. ELTs are currently designed with apertures up to 42m. For these telescopes serious challenges for all parts of the AO system exist. This thesis addresses the challenges for the DM. An 8m class telescope on a representative astronomical site is the starting point. The atmosphere is characterized by the spatial and temporal spectra of Kolmogorov turbulence and the frozen flow assumption. The wavefront fitting error, caused by a limited number of actuators and the temporal error, caused by a limited control bandwidth, are the most important for the DM design. It is shown that ~5000 actuators and 200Hz closed loop bandwidth form a balanced choice between the errors and correct an 8m wavefront in the visible to nearly diffraction limited. An actuator stroke of ~5.6J.!m and ~0.36J.!m inter actuator stroke is thereby needed. Together with the nm's resolution, low power dissipation, no hysteresis and drift, these form the main DM requirements. The design, realization and tests of a new DM that meets these requirements and is extendable and scalable in mechanics, electronics and control to suit further Extremely Large Telescopes (ELTs) is presented. In the DM a few layers are distinguished: a continuous mirror facesheet, the actuator grid and the base frame. In the underlying layer - the actuator grid - low voltage electromagnetic push-pull actuators are located. Identical actuator modules, each with 61 actuators, hexagonally arranged on a 6mm pitch can be placed adjacent to form large grids. The base frame provides a stable and stiff reference. A thin facesheet is needed for low actuator forces and power dissipation, whereby its lower limit is set by the facesheets inter actuator deflection determined by gravity or wind pressure. For both scaling laws for force and dissipation are derived. Minimum power dissipation is achieved when beryllium is used for the mirror facesheet. Pyrex facesheets with 100J.!m thickness are chosen as a good practical, alternative in the prototype development. Struts (00.1 x 8mm) connect the facesheet to the actuators and ensure a smooth surface over the imposed heights and allow relative lateral movement of the facesheet and the actuator grid. Measurements show 3nm RMS surface unflattness from the glued attachment. The stiffness of the actuators form the out-of-plane constraints for the mirror facesheet and determine the mirrors first resonance frequency. and is chosen such that the resonance frequency is high enough to allow the high control bandwidth but not higher that needed to avoid excessive power dissipation and fix points in the surface in case of failure. The electromagnetic variable reluctance actuators designed, are efficient, have low moving mass and have suitable stiffness. Other advantages are the low costs, low driving voltages and negligible hysteresis and drift. The actuators consist of a closed magnetic circuit in which a PM provides static magnetic force on a ferromagnetic core that is suspended in a membrane. This attraction force is increased of decreased by a current through a coil. The actuators are free from mechanical hysteresis, friction and play and therefore have a high positioning resolution with high reproducibility. The actuator modules are build in layers to reduces the number of parts and the complexity of assembly and to improve the uniformity in properties. Dedicated communication and driver electronics are designed. FPGA implemented PWM based voltage drivers are chosen because of their high efficiency and capability to be implemented in large numbers with only a few electronic components. A multidrop LVDS based serial communication is chosen for its low power consumption, high bandwidth and consequently low latency, low communication overhead and extensive possibilities for customization. A flat-cable connects up to 32 electronics modules to a custom communications bridge, which translates the ethernet packages from the control PC into LVDS. Two DMs prototypes were successfully assembled: a 050mm DM with 61 actuators and a 0l50mm DM with 427 actuators. In the second prototype modularity is shown by the assembly of seven identical grids on a common base. The dynamic performance of each actuator is measured, including its dedicated driver and communication. All actuators were found to be functional, indicating that the manufacturing and assembly process is reliable. A nonlinear mathematical model of the actuator was derived describing both its static and dynamic behavior based on equations from the magnetic, mechanic and electric domains. The actuator model was linearized, leading to expressions for the actuator transfer function and properties such as motor constant, coil inductance, actuator stiffness and resonance frequency. From frequency response function measurements these properties showed slight deviations from the values derived from the model, but the statistical spread for the properties was small, stressing the reliability of the manufacturing and assembly process. The mean actuator stiffness and resonance frequency were 0.47kN/m and 1.8kHz respectively, which is close to their design values of 500N/m and 1.9kHz. The time domain response of an actuator to a 4Hz sine voltage was used to determine hysteresis and semi-static nonlinear response of the actuator. This showed the first to be negligible and the second to remain below 5% for ±10J.!m stroke. Measurements showed that in the expected operating range, the total power dissipation is dominated by indirect losses in FPGAs. The static DM performance is validated using interferometric measurements. The measured influence matrix is used to shape the mirror facesheet into the first 28 Zernike modes, which includes the piston term that represents the best flat mirror. The total RMS error is ~25nm for all modes. The dynamic behavior of the DM is validated by measurements. A laser vibrometer is used to measure the displacement of the mirror facesheet, while the actuators are driven by zero-mean, bandlimited, white noise voltage sequence. Using the MOESP system identification algorithm, high-order black-box models are identified with VAF values around 95%. The first resonance frequency identified is 725Hz, and lower than the 974Hz expected from the analytical model. This is attributed to the variations in actuator properties, such as actuator stiffness. The power dissipation in each actuator of the 050mm mirror to correct a typical Von Karmann turbulence spectrum is ~ 1.5m W