Computation of Pressure Loads in the Three-Lobe Supercharger

The compression mechanism in this type of blower is produced by the action of two three-lobe rotors. In this paper the functioning of this kind of blower is analyzed in detail for both the helical and spur rotor types. The analysis allows us to point out specific problems regarding trapped volumes and to design special devices to avoid these problems. The complete dynamics of the loads is determined on this basis, and the performances achieved by helical and spur rotors are compared.

A Compliant, Over-Running Ratchet and Pawl Clutch With Centrifugal Throw-Out

A new compliant, over-running ratchet and pawl clutch with centrifugal throw-out has been developed that drastically reduces the overall part count as compared to traditional ratchet and pawl clutches. Part count for the pawl hub assembly was virtually eliminated by making the hub a single compliant mechanism. This results in large savings in manufacturing, assembly and maintenance costs. Peak torque output for a polypropylene clutch was measured at over 66.2 N-m with an over-running torque measured at < 0.01 N-m. A mathematical model has been developed to predict the rotational speed at which the pawls disengage from the ratchet when free-wheeling. This model was verified experimentally to be accurate within 5.2%. This clutch also demonstrates the advantage of compliant mechanisms to reduce assembly and manufacturing costs.

Geometric Criteria for Gouge-Free Three-Axis Milling of Sculptured Surfaces

The paper presents a geometric investigation of collision-free 3-axis milling of surfaces. We consider surfaces with a global shape condition: they shall be interpretable as graphs of bivariate functions or shall be star-shaped with respect to a point. If those surfaces satisfy a local millability criterion involving curvature information, it is proved that this implies globally gouge-free milling. The proofs are based on general offset surfaces. The results can be applied to tool-motion planning and the computation of optimal cutter shapes.

Architecture Optmization of a 3-DOF Parallel Mechanism

This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms

The displacement analysis problem for planar and spatial mechanisms can be written as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper presents a new approach to displacement analysis using the reduced Gröbner basis form of a system of equations under degree lexicographic (dlex) term ordering of its monomials and Sylvester’s Dialytic elimination method. Using the Gröbner-Sylvester hybrid approach, a finitely solvable system of equations F is transformed into its reduced Gröbner basis G using dlex term ordering. Next, using the entire or a subset of the set of generators in G, the Sylvester’s matrix is assembled. The vanishing of the resultant, given as the determinant of Sylvester’s matrix, yields the necessary and sufficient condition for the polynomials in G (as well as F) to have a common factor. The proposed approach appears to provide a systematic and rational procedure to the problem discussed by Roth (1994) dealing with the generation of (additional) equations for constructing the Sylvester’s matrix. Three examples illustrating the applicability of the proposed approach to displacement analysis of planar and spatial mechanisms are presented. The first and second examples deal with forward displacement analysis of the general 6-6 Stewart mechanism and the 6-6 Stewart platform, whereas the third example deals with the determination of the input-output polynomial of a 8-link 1-DOF mechanism which does not contain any 4-link loops.

A New Inertia-Based Linear Stepper Motor for Micro-Surgical Procedures

A new hand held surgical device intended to aid physicians in microsurgery is reported. This device provides a means for delivering small implants through the use of a precision motion linear stepper motor fabricated from silicon and piezoelectric components. The stepper motor described here utilizes the inertial properties of a moving mass as part of the actuation process. Micro Electromechanical Systems-based (MEMS) technology is used in building the device. Test instruments have delivered over fifty implants with consistent performance. Typically the test instruments have attained 1.2 mm/s advancement speeds against 3 Newton resistance loads, a maximum output force of 4.6 Newtons, and maximum total displacement of 38 mm.

Design of Electrostatic Micro Mirrors for Improved Stability Though Surface Contact

There exists a need to stabilize the electrostatic actuation commonly used in Micro-Electro-Mechanical Systems (MEMS). Most electrostatically actuated MEMS devices act as variable capacitors with varying gap between the charged conductors. Electrostatic force in these devices is a nonlinear attractive force between the conductors resulting in a complex dynamic system. These systems are stable for only a small portion of the initial gap. In this paper a design method is presented for electrostatic micro-mirrors with improved stability. Controllable, stable electrostatic actuation can be achieved through surface contact between the two conductors. Once in contact with the surface, the compliance of the structure is used to stabilize the electrostatic actuation over a long range of motion. Beam based variable angle mirrors were designed and fabricated using the Multi-User MEMS Process at MCNC technology center. The design methods for stable electrostatic actuation were tested on these mirrors. Some characteristics are noted and their implementation into future designs is discussed.

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

Using Dual Cam Tracks for High Speed Rigid Body Motion

Rigid Body Motion has long been one of the standard problems for kinematicians. For high speed transfer rates, an industrial example of using a dual cam track system to achieve better performance is documented. The dual track establishes both a positional and orientational location of the followers. The selection of this mechanism type is discussed.