A Hydraulic Micromanipulator

For biological experiments requiring manipulations under a microscope, it is necessary to have remote control for the manipulator. Available systems offer the required accuracy at a high cost. Passive micromanipulators are economical but are deficient in performance, the most serious defects being the inability to attenuate operator-induced vibrations and lack of speed control The manipulator described in this paper provides versatile remote control and may be constructed economically.

A Hydraulic Micromanipulator

For biological experiments requiring manipulations under a microscope, it is necessary to have remote control for the manipulator. Available systems offer the required accuracy at a high cost. Passive micromanipulators are economical but are deficient in performance, the most serious defects being the inability to attenuate operator-induced vibrations and lack of speed control The manipulator described in this paper provides versatile remote control and may be constructed economically.

Blade manipulators in turbulent channel flow

We report here the results of a series of careful experiments in turbulent channel flow, using various configurations of blade manipulators suggested as optimal in earlier boundary layer studies. The mass flow in the channel could be held constant to better than 0.1%, and the uncertainties in pressure loss measurements were less than 0.1 mm of water; it was therefore possible to make accurate estimates of the global effects of blade manipulation of a kind that are difficult in boundary layer flows. The flow was fully developed at the station where the blades were mounted, and always relaxed to the same state sufficiently far downstream. It is found that, for a given mass flow, the pressure drop to any station downstream is always higher in the manipulated than in the unmanipulated flow, demonstrating that none of the blade manipulators tried reduces net duct losses. However the net increase in duct losses is less than the drag of the blade even in laminar flow, showing that there is a net reduction in the total skin friction drag experienced by the duct, but this relief is only about 20% of the manipulator drag at most.

Dynamical Resolution of Redundancy for Robot Manipulators

A large class of work in the robot manipulator literature deals with the kinematical resolution of redundancy based on the pseudo-inverse of the manipulator Jacobian. In this paper an alternative dynamical approach to redundancy resolution is developed which utilizes the mapping between the actuator torques and the acceleration of the end-effector, at a given dynamic state of the manipulator. The potential advantages of the approach are discussed and an example of a planar 3R manipulator following a circular end-effector trajectory is used to illustrate the proposed approach as well as to compare it with the more well-known approach based on the pseudo-inverse.

Kinematic analysis and design of articulated manipulators with joint motion constraints

For an articulated manipulator with joint rotation constraints, we show that the maximum workspace is not necessarily obtained for equal link lengths but is also determined by the range and mean positions of the joint motions. We present expressions for sectional area, workspace volume, overlap volume and work area in terms of link ratios, mean positions and ranges of joint motion. We present a numerical procedure to obtain the maximum rectangular area that can be embedded in the workspace of an articulated manipulator with joint motion constraints. We demonstrate the use of analytical expressions and the numerical plots in the kinematic design of an articulated manipulator with joint rotation constraints.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Synthesis of workspaces of planar manipulators with arbitrary topology using shape representation and simulated annealing

This paper presents a general methodology for the synthesis of the external boundary of the workspaces of a planar manipulator with arbitrary topology. Both the desired workspace and the manipulator workspaces are identified by their boundaries and are treated as simple closed polygons. The paper introduces the concept of best match configuration and shows that the corresponding transformation can be obtained by using the concept of shape normalization available in image processing literature. Introduction of the concept of shape in workspace synthesis allows highly accurate synthesis with fewer numbers of design variables. This paper uses a new global property based vector representation for the shape of the workspaces which is computationally efficient because six out of the seven elements of this vector are obtained as a by-product of the shape normalization procedure. The synthesis of workspaces is formulated as an optimization problem where the distance between the shape vector of the desired workspace and that of the workspace of the manipulator at hand are minimized by changing the dimensional parameters of the manipulator. In view of the irregular nature of the error manifold, the statistical optimization procedure of simulated annealing has been used. A number of worked-out examples illustrate the generality and efficiency of the present method. (C) 1998 Elsevier Science Ltd. All rights reserved.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Towards the concept of hydrodynamic cavitation control

A careful study of the existing literature available in the field of cavitation reveals the potential of ultrasonics as a tool for controlling and, if possible, eliminating certain types of hydrodynamic cavitation through the manipulation of nuclei size present in a flow. A glass venturi is taken to be an ideal device to study the cavitation phenomenon at its throat and its potential control. A piezoelectric transducer, driven at the crystal resonant frequency, is used to generate an acoustic pressure field and is termed an �ultrasonic nuclei manipulator (UNM)�. Electrolysis bubbles serve as artificial nuclei to produce travelling bubble cavitation at the venturi throat in the absence of a UNM but this cavitation is completely eliminated when a UNM is operative. This is made possible because the nuclei, which pass through the acoustic field first, cavitate, collapse violently and perhaps fragment and go into dissolution before reaching the venturi throat. Thus, the potential nuclei for travelling bubble cavitation at the venturi throat seem to be systematically destroyed through acoustic cavitation near the UNM. From the solution to the bubble dynamics equation, it has been shown that the potential energy of a bubble at its maximum radius due to an acoustic field is negligible compared to that for the hydrodynamic field. Hence, even though the control of hydrodynamic macro cavitation achieved in this way is at the expense of acoustic micro cavitation, it can still be considered to be a significant gain. These are some of the first results in this direction.

Redundancy resolution using a tractrix and its application to real-time simulations of hyper-redundant manipulators, snakes and tying of knots

To realistically simulate the motion of flexible objects such as ropes, strings, snakes, or human hair,one strategy is to discretise the object into a large number of small rigid links connected by rotary or spherical joints. The discretised system is highly redundant and the rotations at the joints (or the motion of the other links) for a desired Cartesian motion of the end of a link cannot be solved uniquely. In this paper, we propose a novel strategy to resolve the redundancy in such hyper-redundant systems.We make use of the classical tractrix curve and its attractive features. For a desired Cartesian motion of the `head'of a link, the `tail' of the link is moved according to a tractrix,and recursively all links of the discretised objects are moved along different tractrix curves. We show that the use of a tractrix curve leads to a more `natural' motion of the entire object since the motion is distributed uniformly along the entire object with the displacements tending to diminish from the `head' to the `tail'. We also show that the computation of the motion of the links can be done in real time since it involves evaluation of simple algebraic, trigonometric and hyperbolic functions. The strategy is illustrated by simulations of a snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator.

An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Tip Motion Control and Scanning of a Reorientable Micromanipulator With Axially Located Tip

Two-axis micromanipulators, whose tip orientation and position can be controlled in real time in the scanning plane, enable versatile probing systems for 2.5-D nanometrology. The key to achieve high-precision probing systems is to accurately control the interaction point of the manipulator tip when its orientation is changed. This paper presents the development of a probing system wherein the deviation in the end point due to large orientation changes is controlled to within 10 nm. To achieve this, a novel micromanipulator design is first proposed, wherein the end point of the tip is located on the axis of rotation. Next, the residual tip motion caused by fabrication error and actuation crosstalk is modeled and a systematic method to compensate it is presented. The manipulator is fabricated and the performance of the developed scheme to control tip position during orientation change is experimentally validated. Subsequently, the two-axis probing system is demonstrated to scan the full top surface of a micropipette down to a diameter of 300 nm.

Whole arm manipulation using closed and hybrid planar chains: A kinematic study

This paper studies planar whole arm manipulation of a circular object using closed loop and hybrid manipulators. The manipulation is simple with fewer degrees of actuation than the task space. This is an useful operation if the initial and final positions of the object are on the same surface. Closed loop manipulator is a 4/5 bar mechanism. In hybrid manipulators a open loop manipulator with 3/4 links is attached to the floating link of 4/5 bar mechanism. The mobility analysis is carried out to find the connectivity of the object with reference to frame. The manipulation (forward kinematics) starts from a given configuration of the object and the manipulator. In hybrid manipulators determination of initial configuration involves inverse kinematics of open loop manipulator. The input joint velocities are used to demonstrate the manipulation. Conditions are specified for prehensile manipulation.