Ian S. Fischer

Numerical analysis of displacements in spatial mechanisms with ball joints

Abstract The ball joint, often referred to as a spherical or ‘S’ joint is modeled using dual-number coordinate-transformation matrices. The joint consists of concave and convex spherical surfaces engaged to prevent translations but allowing three degrees of freedom, all of which are rotations. Derivative-operator matrices to be used in the Fischer–Paul adaptation of the Uicker–Denavit–Hartenberg numerical scheme for displacement analysis of spatial mechanisms are developed. The generalized slider-crank (CSSP) mechanism is presented as an example featuring ball joints where coordinate-transformation matrices modeling links with ball joints are used in a concatenation with analogous matrices modeling links with revolute, prismatic or cylindrical joints to analyze the displacements.

Numerical Analysis of Displacements in a Tracta Coupling

Abstract. Derivative operators are developed so that the Fisher–Paul dual-number version of the Uicker–Denavit– Hartenberg iteration scheme for computing displacements in spatial mechanisms can be applied to the Tracta coupling. The constant-velocity input-output characteristic of the Tracta coupling is shown and the intermediate-joint displacements are investigated.

Velocity analysis of mechanisms with ball joints

Abstract A procedure is developed for analyzing velocities in spatial mechanisms with ball joints has been designed for practical computerization. The correspondence between the calculated velocities in a ball joint and the time changes of the physical displacements is clarified. The methodology is demonstrated using the RSPC mechanism which has seen commercial application as a washing-machine agitator mechanism.

The dual angle and axis of a screw motion

Abstract The dual-number coordinate transformation matrix representing a screw motion through a general axis in space has been developed. A method for determining the axis and screw motion associated with a given dual-number coordinate transformation is also dealt with. Developing the dual-number matrix and determining the rotation angle from a given-number matrix is done in a manner analogous to that for handling simple rotations about axes intersecting the origin of the coordinate frame corresponding to the original position. By using dual-number methods, the axis of the motion may be any line in space and the translation along that axis can be considered when a screw motion has occurred.

Static Equilibrium of Spatial Mechanisms With Cylindrical Joints

The components of force and torque acting on a joint of a link in static equilibrium are partitioned according to the type of joint so that the equations of static equilibrium can be set up automatically by computer where the type of each joint has been specified in the input data. Special attention is given to the cylindrical joint, and the implications of the geometry of an intermediate link with a cylindrical joint on both ends are examined. While the methodology is demonstrated for the RCCC mechanism, which features a revolute input joint and cylindrical intermediate and output joints, it is adaptable to closed-loop mechanisms of binary links with any kind of joint in any position.

A Complete Notation for Dual Velocity

A notation is developed which specifies a dual velocity without ambiguity. The point of interest, the moving body, the reference body, and the system of unit vectors in which a dual velocity is expressed are all clearly indicated. The equivalence between the equation of transformation and the coordinate-transformation matrix formulation is shown. Equations are developed to enable calculation of the dual velocity at a point in a body given the dual velocity at any other point, to change the system of unit vectors in which a dual velocity is expressed, and to calculate relative velocities. Use of these equations is demonstrated in an example using the spatial four-bar mechanism which is specialized to the Cardan joint and the wobble-plate mechanism, and the effect of some tolerance errors on output velocity is shown.

NON-INTRUSIVE PARTICLE TRACKING SYSTEM FOR PARTICULATE FLOWS AND VIBRATED GRANULAR BEDS

ABSTRACT A unique, non-intrusive particle tracking system based on the principle of magnetic induction coupling is presented. In this system, small transmitters are mounted inside the particle being tracked, and a set of receiving antennae surrounding the experimental apparatus. Based on the measured signals for induced voltages in the antennae, the three-dimensional trajectory of the particle is resolved by solving the inverse problem. The experimental system development, including hardware and data acquisition aspects, is also described. The system was tested through test experiments which include a real time trajectory. The results indicate that a system with three mutually orthogonal transmitters provides accurate results. This system is ideally suited for experimental investigation of segregation in vibrated beds. Results for such study of real trajectories of a single sphere rising in a mass of other spheres in a vibrated bed are also shown to demonstrate phenomena such as period doubling and bifurc...

Modeling the Plane Joint

The plane joint, often referred to as the “E” joint is modeled using dual-number coordinate-transformation matrices. The joint consists of two flat surfaces held in contact so that three degrees of freedom are allowed, two translations and a rotation. The swash-plate mechanism is used as an example of a mechanism featuring the plane joint.

Static Analysis of Mechanisms with Ball Joints

Abstract Equations of static equilibrium are developed for the ball joint, which is a complex joint in that the coordinates in which its displacements are naturally expressed are stated in different coordinate frames. The implications of this are examined, and the generalized slider-crank mechanism (RSSP mechanism) is given as an example.

PIV Measurement of the Transient Fluid Flow due to the Adsorption of Particles

The particle image velocimetry (PIV) technique is used to study the physics of particle adsorption and the spontaneous dispersion of powders that occurs when particles come in contact with a fluid-liquid interface. The dispersion can occur so quickly that it appears explosive, especially for small particles on the surface of mobile liquids like water. The measurements show that the adsorption of a spherical particle causes an axisymmetric streaming flow about the vertical line passing through the center of the particle. The fluid directly below the particle rises upward, and near the surface, it moves away from the particle. The flow, which develops within a fraction of second after the adsorption of the particle, persists for several seconds. The flow strength, and the volume over which it extends, decrease with decreasing particle size. The streaming flow induced by the adsorption of two or more particles is a combination of the flows which they induce individually.Copyright