Institute for Systems Research
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Item Workspace and Singularity Analysis of a Novel Six-DOF Parallel Minimanipulator(1993) Tahmasebi, F.; Tsai, L-W.; ISRWorkspace and singularity analysis of a novel three-limbed, six degree-of-freedom (DOF) minimanipulator is presented. The minimanipulator limbs are inextensible and its actuators are base-mounted. The lower ends of the limbs are connected to bidirectional linear stepper motors which are constrained to move on a base plane. The minimanipulator is capable of providing high positional resolution and high stiffness. A discretization algorithm is used to determine the minimanipulator workspace for a given platform orientation. The algorithm uses the bisection method and the inverse kinematics of the minimanipulator to find the cross-sectional boundaries of the workspace. Necessary and sufficient conditions for both inverse and direct kinematics singularities are obtained. The latter which could occur within the minimanipulator workspace is discussed in more detail. The Jocobian matrix is used to obtain some of the singularities. An alternative approach is used to determine additional singular configurations.Item A CAD System for the Optimization of Gear Ratios for Automotive Automatic Transmissions(1992) Mogalapalli, Srinivas N.; Magrab, Edward B.; Tsai, L-W.; ISRAn interactive design system has been developed for the design of automatic automotive transmission gear trains that can provide at least three forward and one reverse speed ratios. This user- friendly windowing system can access help files, display the functional representation of a mechanism, optimize the gear ratios and present the numerical results. The optimization procedure to find the optimum gear ratios and the corresponding number of gear teeth uses the Augmented Lagrangian Multiplier Method and can be applied to all epicyclic gear trains having two sets of three gears in which a ring gear is connected to a sun gear through a planetary gear. The Simpson and General Motors THM 440 gear trains are used to demonstrate the methodology. The gear teeth combinations are found such that they achieve the optimized gear ratios to within ﯠ1% and satisfy the geometric constraints. PHIGS graphics functions are used in program routines to display the functional schematic of an epicyclic gear train on the computer screen. These routines are written in such a manner that other types of gear combinations can be displayed by simply adding additional modules to represent these new gear elements.Item Kinematic Synthesis of Tendon-Driven Manipulators with Isotropic Transmission Characteristics(1992) Ou, Y-J.; Tsai, L-W.; ISRThis paper presents a methodology for kinematic synthesis of tendon-driven manipulators with isotropic transmission characteristics. The force transmission characteristics, from the end-effector space to the actuator space, has been investigated. It is shown that tendon forces required to act against externally applied forces are functions of the structure matrix, its null vector, and the manipulator Jocobian matrix. Design equations for synthesizing a manipulator to possess isotropic transmission characteristics are derived. An isotropic transmission is defined as one for which the product of the structure matrix and Jacobian matrix has a unity condition number, and the direction of the null vector points in the [1, 1, ..., 1]T direction. Two examples are used to demonstrate the methodology. It is shown that manipulators which possess isotropic transmission characteristics do have much better force distribution among their tendons.Item Jacobian and Stiffness Analysis of a Novel Class of Six-DOF Parallel Minimanipulators(1992) Tahmasebi, F.; Tsai, L-W.; ISRThe Jacobian and stiffness matrices of two types of novel, six- DOF parallel minimanipulators are derived. A minimanipulator consists of three inextensible limbs, each of which is driven by a two-DOF driver. Bilinear stepper motors are used as drivers in the first type minimanipulator, whereas five-bar linkages are used as drivers in the second type minimanipulator. all of the minimanipulator actuators are base-mounted. Inextensible limbs (and five-bar linkage drivers in the second type minimanipulator) improve positional resolution and stiffness of the minimanipulators in certain directions. It is shown that, at the central configuration, the stiffness matrix of the first type minimanipulator can be diagonalized (decoupled). It is also shown that the first type minimanipulator can be designed to posses direct or torsional isotropic stiffness properties. Moreover, guidelines for designing the drivers of the second type minimanipulator are established.Item Jacobian and Stiffness Analysis of a Novel Six-DOF Parallel Minimanipulator(1992) Tahmasebi, F.; Tsai, L-W.; ISRThe Jacobian and stiffness matrices of a novel, six-DOF parallel minimanipulator are derived. The minimanipulator consists of three inextensible limbs, each of which is driven by a five-bar linkage to improve its positional resolution and stiffness. All of the minimanipulator actuators are base-mounted. It is shown that, at the central configuration of the minimanipulator workspace, the stiffness matrix can be diagonalized (decoupled). It is also shown that the minimanipulator can be designed to posses direct or torsional isotropic stiffness properties. Moreover, velocity relationships for the minimanipulator drivers are derived and guidelines for obtaining high stiffness are established.Item Closed-Form Direct Kinematics Solution of a New Parallel Minimanipulator(1991) Tahmasebi, F.; Tsai, L-W.; ISRClosed-form direct kinematics solution of a new three-limbed six- degree-of-freedom minimanipulator is presented. Five-bar linkages and inextensible limbs are used in synthesis of the minimanipulator to improve its positional resolution and stiffness. All of the minimanipulator actuators are based- mounted. Kinematic inversion is used to reduce the direct kinematics of the minimanipulator to an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the moving platform. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. Furthermore, it is proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs. A numerical example is also presented and the results are verified y an inverse kinematics analysis.Item Design of a Crank-and-Rocker Driven Pantograph: A Leg Mechanism for the University of Maryland's 1991 Walking Robot(1991) Williams, R.P.; Tsai, L-W.; Azarm, Shapour; ISRThe National Aeronautics and Space Administration has been funding university research into flexible, six-legged walking machines capable of exploring alien terrain. This research has led to a progressive new look at standard four bar mechanisms.Four bar mechanisms, by definition, consist of a crank link, coupler link, rocker link and fixed (ground) link. The passive role of the coupler link, in traditional four bar mechanisms, can be reversed so that the coupler becomes the transmission link. This is achieved by replacing the coupler with an oblique triangular link. The internal angles of the modified coupler can be varied to create an array of continuous, ovoid paths at the disjointed vertex of the triangle.
Attaching a pantograph mechanism to the modified coupler's trace point amplifiers and translates the ovoid path. The combination of these two mechanisms provides a stable, one degree of freedom walking path which emulates that of humans. This mechanism can therefore be used as a robotic leg.
A second degree of freedom is obtained by attaching an adjacent link to the pantograph mechanism which raises or lowers the walking path without effecting its shape or magnitude. This is used for climbing and maneuvering amidst rugged terrain.