Institute for Systems Research
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Item On the Stiffness of a Novel Six-DOF Parallel Minimanipulator(1995) Tahmasebi, F.; Tsai, L.W.; ISRThe dimensionally-uniform Jacobian matrix of a novel three- limbed, six degree-of-freedom (DOF) minimanipulator is used to derive its dimensionally-uniform stiffness matrix.The minimanipulator limbs are inextensible and its actuators are base-mounted. The lower ends of the limbs are connected to bi- directional linear stepper motors which are constrained to move on a base plane. The minimanipulator is capable of providing high positional resolution and high stiffness.
It is shown that, at a central configuration, the stiffness matrix of the minimanipulator can be decoupled (diagonalized), if proper design parameters are chosen. It is also shown that the stiffness of the minimanipulator is higher than that of the Stewart platform. Guidelines for obtaining large minimanipulator stiffness values are established.
Item Kinematic Synthesis and Analysis of a Novel Class of Six-DOF Parallel Minimanipulators(1993) Tahmasebi, F.; Tsai, L-W.; ISRA new class of six-degree-of-freedom (six-DOF) parallel minimanipulators is introduced. The minimanipulators are designed to provide high resolution and high stiffness in fine- manipulation operations. Two-DOF planar mechanisms (e.g., five- bar linkages, pantographs) and inextensible limbs are used to improve positional resolution and stiffness of the minimanipulators. The two-DOF mechanisms serve as drivers for the minimanipulators. The minimanipulators require only three inextensible limbs and unlike most of the six-limbed parallel manipulators, their direct kinematics can be reduced to solving a polynomial in a single variable. All of the minimanipulator actuators are base-mounted. As a result, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained.Inverse kinematics of the minimanipulators has been reduced to solving three decoupled quadratic equations, each of which contains only one unknown.
Kinematic inversion is used to reduce the direct kinematics of the minimanipulator to an eighth- degree polynomial in the square of a single variable. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. 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.
The Jacobian and stiffness matrices of two types of minimanipulators are derived. It is shown that, at a central configuration, the stiffness matrix of the first type minimanipulator (driven by bidirectional linear stepper motors) can be decoupled, if proper design parameters are chosen. It is also shown that the stiffness of the minimanipulators is higher than that of the Stewart platform. Guidelines for obtaining large stiffness values and for designing the drivers of the second type minimanipulator (simplified five-bar linkages) are established.
An algorithm is developed to determine the workspace of the minimanipulators. Given any orientation for the output link, three-dimensional representation of the workspace is obtained. Guidelines for avoiding discontinuities inside of the workspace are established.
Necessary and sufficient conditions for both inverse and direct kinematics singularities of the minimanipulators are obtained. Guidelines for avoiding direct kinematics singularities, which occur within the minimanipulator workspace, are established.
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 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.