Nonlinear Generalization of Den Hartog's Equal-Peak Method

Generally, adjustment of gravity equilibrator to a new payload requires energy, e.g. to increase the pre-load of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.© 2009 ASME

Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators

This article discusses the development of statically balanced spatial parallel platform mechanisms. A mechanism is statically balanced if its potential energy is constant for all possible configurations. This property is very important for robotic manipulators with large payloads, since it means that the mechanism is statically stable for any configuration, i.e., zero actuator torques are required whenever the manipulator is at rest. Furthermore, only inertial forces and moments have to be sustained while the manipulator is moving. The application that motivates this research is the use of parallel platform manipulators as motion bases in commercial flight simulators, where the weight of the cockpit results in a large static load. We first present a class of spatial parallel platform mechanisms that is suitable for static balancing. The class of mechanisms considered is a generalization of the manipulator described by Streit (1991, Spatial Manipulator and Six Degree of Freedom Platform Spring Equilibrator Theory, in Second National Conference on Applied Mechanisms and Robotics, VIII.B, pp. 1-1-1-6). Then sufficient conditions on the kinematic parameters that guarantee static balancing are derived for this class. Finally a particular mechanism is studied in more detail to show the practicability of its design.

Static balancing of spatial parallel Platform mechanisms-revisited

This article describes the development of a mobile arm support for people with muscular diseases. The arm support is spring-balanced, with special attention on reduction of operating effort (high balancing quality and low friction), functionality (large range of motion), and aesthetics (inconspicuous design). The spring settings can be adjusted for wearing heavier clothing or picking up an object, a function that can also be used for moving up or down. The device levels itself automatically to compensate for uneven floors, a function that can be overruled to assist forward/backward motion of the arm. Thus, the balancer can compensate for the weight of the arm and be adjusted to generate force to a limited (safe) extent. The principle and design of the mechanism are presented and preliminary field trial results are given. Two users report on 6 months of continuous use of the arm support in their home and social environments.

/pdf/principle-and-design-of-a-mobile-arm-support-for-people-with-2mb5l88qvz.pdf

Principle and design of a mobile arm support for people with muscular weakness

Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs

An open-loop nonlinear control strategy applied to a hinged-hinged shallow arch, subjected to a longitudinal end-displacement with frequency twice the frequency of the second mode (principal parametric resonance), is developed. The control action?a transverse point force at the midspan?is typical of many single-input control systems; the control authority onto part of the system dynamics is high whereas the control authority onto some other part of the system dynamics is zero within the linear regime. However, although the action of the controller is orthogonal, in a linear sense, to the externally excited first antisymmetric mode, beneficial effects are exerted through nonlinear actuator action due to the system structural nonlinearities. The employed mechanism generating the effective nonlinear controller action is a one-half subharmonic resonance (control frequency being twice the frequency of the excited mode). The appropriate form of the control signal and associated phase is suggested by the dynamics at reduced orders, determined by a multiple-scales perturbation analysis directly applied to the integral-partial-differential equations of motion and boundary conditions. For optimal control phase and gain?the latter obtained via a combined analytical and numerical approach with minimization of a suitable cost functional?the parametric resonance is cancelled and the response of the system is reduced by orders of magnitude near resonance. The robustness of the proposed control methodology with respect to phase and frequency variations is also demonstrated. ©2002 ASME

Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach

A new open-loop control strategy applied to a planar pendulum subjected to the most severe com bination of base excitations, horizontal motion at the primary-resonance frequency, and vertical motion at the principal-parametric resonance frequency is developed. The control action is typical of many single-input control systems; the control authority in one direction (horizontal) is high, and the control authority in the or thogonal direction (vertical) is zero in a linear sense. Although the action of the controller is linearly orthog onal to part (vertical or parametric) of the system excitation, effects are transferred to this direction through nonlinear actuator action. Proper enhancement of the control input allows the nonlinear action to provide con trol authority over the parametric excitation. The dynamics at reduced orders, determined by a multiple-scales perturbation analysis, suggest the appropriate form for the control enhancement. The normal form of the sys tem provides information about how ea...

Open-Loop Resonance-Cancellation Control for a Base-Excited Pendulum

Velocity analysis of parallel manipulators by truss transformations

A passive vibration absorber for reducing the motion of a planar pendulum is developed. The system is excited by the horizontal motion of the support. The design transforms the original one-degree-of- freedom pendulum into a double pendulum by adding a small secondary pendulating sacrificial mass between the main system and the base excitation point and two pretensioned springs that generate negative restoring moments (i.e., of opposite sign to that of the gravity-induced restoring moments). Optimal conditions for enhancing the transfer of energy from the main (lower) to the secondary (upper) pendulum are sought. The damping is assumed to be of a linear viscous-type. Due to the action of the springs, the transfer function between the pendulation angle of the main system and the disturbance, in the undamped linearized case, can be reduced to zero for any excitation frequency This is accomplished by requiring that the two spring stiffnesses satisfy an algebraic tuning relation. Due to the inherent inertial ...

R. Randall Soper

Papers

Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach

Open-Loop Resonance-Cancellation Control for a Base-Excited Pendulum

Velocity analysis of parallel manipulators by truss transformations

A Nonclassical Vibration Absorber for Pendulation Reduction

Vibration of Nearly Perfect Spring Equilibrators