Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.

Identification and Compensation of Geometric and Elastic Errors in Large Manipulators: Application to a High Accuracy Medical Robot

A method is presented to identify the source of end-effector positioning errors in large manipulators using experimentally measured data. Both errors due to manufacturing tolerances and other geometric errors and elastic structural deformations are identified. These error sources are used to predict, and compensate for, the end-point errors as a function of configuration and measured forces. The method is applied to a new large high accuracy medical robot. Experimental results show that the method is able to effectively correct for the errors in the system.

Analytical Model Method for Dynamics of N-Celled Tetrahedron-Tetrahedron Variable Geometry Truss Manipulators

In this paper some fundamental formulae are derived for tetrahedron-based variable geometry truss manipulator which is composed of a series of tetrahedrons stacked upon each other such that one link in each cell is made variable on length. Analytical model for dynamics of the manipulator is established, and expressions in numeric-symbolic form of model matrices are derived. An example is given for illustration.

An Assessment of Geometric Methods in Trajectory Synthesis for Shape Creating Operations

This paper presents an assessment of the steps involved in trajectory synthesis (e.g., trajectory layout, trajectory generation, trajectory spacing, trajectory postprocessing, and trajectory physics) for shape creating manufacturing operations, e.g., rapid prototyping, milling, electrical discharge machining. The rationale for this paper is that the trajectory plays an important role in determining the productivity as explained below. Shape creating manufacturing operations are those that make use of a “tool” which operates on a “workpiece” to create the desired shape. The tool operates on the workpiece as dictated by the trajectory of the tool, resulting in the manufactured shape. Often, the geometric and functional properties of the end product are dependent on the trajectory of the tool. Moreover, the trajectory dictates the accuracy of the end product and the time taken to manufacture the product. Recognizing the important contribution of the trajectory in shape creating operations, this paper focuses on trajectory synthesis.

Kinematically Generated Dual Tensor-Product Surfaces

This paper takes advantage of the duality between point and plane geometries and studies a class of tensor-product surfaces that can be generated kinematically as surfaces enveloped by a plane under two-parameter rational Bézier motions. The results of this cross-disciplinary work, between the field of Computer Aided Geometric Design and Kinematics, can be used as a basis for studying geometric and kinematic issues associated with the design and manufacture of freeform surfaces.

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.