Optimal Kinematic Design Research Articles

Kinematic optimal design of a new parallel-type rolling mill: paramill

In this paper, a kinematic optimal design of a new parallel-type rolling mill based upon two Stewart platform manipulators is investigated. To provide the end-effector (work roll) with sufficient d.o.f. and to achieve the structural stability of each stand, a parallel manipulator with six legs is considered. The objective of this new parallel-type rolling mill is to pursue an integrated control of the strip thickness, strip shape, pair-crossing angle, uniform wear of the rolls and strip tension. By splitting the weighted Jacobian matrices into two parts, the linear velocity, angular velocity, force and moment transmissibilities are analyzed. A manipulability measure, as the ratio of the manipulability ellipsoid volume and the condition number of a split Jacobian matrix, is defined. The two kinematic parameters, the radius of the base and the angle between two neighboring joints, are optimally designed by maximizing the global force manipulability measure defined in the entire workspace. The maximum exerting force needed in hydraulic actuators is also calculated using the kinematic structure determined and the Plücker coordinates introduced. Simulation results are provided.

A real‐coded genetic optimal kinematic design of a Stewart fine tuning platform for a large radio telescope

AbstractA real‐coded genetic design methodology for an optimal kinematic Stewart platform is presented in this article. The Jacobian matrix connecting the dexterity performance of the parallel platform is first deduced, and then the condition number of Jacobian matrix is employed as the objective function to implement the optimal kinematic design of Stewart fine tuning platform for a large spherical radio telescope. A niched‐penalty approach is used to transform this optimal kinematic design problem to an unconstrained one, and a niching technique and the dynamic mutation operator are applied. A kinematic accuracy comparison of the genetically designed Stewart fine tuning platform with the quasi‐Newtonian designed platform is made. The comparison results have shown that the kinematic accuracy of the genetically designed Stewart fine tuning platform has a much higher accuracy and compact structure than that of the quasi‐Newtonian designed platform, which guarantees the implementation of high accuracy requirement of trajectory tracking and reduces the disturbance of random wind for large radio telescopes. © 2001 John Wiley & Sons, Inc.

Optimal kinematic design of a haptic pen

This paper investigates the performance demands of a haptic interface and shows how this information can be used to design a suitable mechanism. A design procedure, previously developed by the authors (1996), consisting of a global isotropy index and a discrete optimization algorithm, allows one to compare a range of geometric variables, actuator scale factors, and even different robot devices for optimum performance. The approach is used to compare the performance of three 6-DOF robots including two well-known parallel platform robots and a novel hybrid robot called the Twin-Pantograph in terms of their semi-dextrous workspaces and static force capabilities. Since the Twin-Pantograph yields the best results, its design is refined to address practical constraints and it is implemented as a haptic pen. The performance of the resulting design is analysed and presented.

Optimal Kinematic Design of Haptic Device for Precision Task

Optimal Kinematic Design of Haptic Device for Precision Task

Task-specific optimal simultaneous kinematic, dynamic, and control design of high-performance robotic systems

A task-specific optimal simultaneous kinematic, dynamic and control design approach is proposed for high-performance computer-controlled machines, such as robots. This mechatronics design approach is based on the trajectory pattern method and a fundamentally new design philosophy that such machines, in general, and ultrahigh-performance machines, in particular, must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic, and control parameters are optimized simultaneously with the parameters that describe a selected trajectory pattern with which the desired class(es) of task(s) can best be performed. In one example, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. Based on the developed design methodology, a two-degrees-of-freedom robot manipulator with a closed-loop chain is optimally designed and constructed for point-to-point motions. The preliminary results of experiments indicate that the robot can, in fact, execute point-to-point motions rapidly and with minimal residual vibration. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

Optimal kinematic design of an anthropomorphic robot module with redundant actuators

Motivated by the redundant actuation mode of the human body, which produces several unique functions that general robotic mechanisms cannot generate, an anthropomorphic robot module resembling the musculoskeletal structure of the human upper limb is investigated. Specifically, optimal kinematic design of the proposed robot module is treated. Initially, the kinematic model of the robot module is obtained, and five design indices are then defined based on the kinematic model. These indices include workspace area, Jacobian isotropic index, maximum force transmission ratio, and gradient design indices for the Jacobian isotropic index and the maximum force transmission ratio. To deal with this multi-criteria based design, a kinematic composite design index (KCDI) is introduced which combines several individual design indices as a unique design index using the max-min principle of fuzzy theory. Two KCDIs are considered as objective functions in the kinematic optimization. One includes the three design indices without the two gradient design indices, and the other includes all five design indices. As a result of optimization based on the two KCDIs, two sets of nine optimal kinematic design parameters are obtained. The two designs are compared with respect to three operational performances: maximum load handling capacity, maximum hand velocity and maximum hand acceleration capability. Optimal actuator sizes of the two designs are also compared for the given specifications of three operational performances. The design taking into account all five design indices shows superior operational performances and smaller actuator sizes than those of the design ignoring gradient design indices.

Kinematic Isotropy and the Optimum Design of Parallel Manipulators

The differential kinematic equations (DKE) of parallel manip ulators usually involve two Jacobian matrices that, depending on the role they play in the kinetostatic transformation between the joint and Cartesian variables, are commonly referred to as the forward and the inverse Jacobians. In this article, we make use of the special structure of these Jacobians to define a set of conditions under which a parallel manipulator can be rendered isotropic. These conditions are general, and pro vide a systematic method for the optimum kinematic design of parallel manipulators, with or without introducing structural constraints. The application of the proposed conditions is illus trated in detail through a few examples, one of which pertains to the design of a 6-DOF isotropic parallel manipulator.

Kinematic design optimization of the variable lead screw mechanism with cone meshing element

The variable lead screw mechanism is proven to be an overconstrained mechanism. Transmission quality of the mechanism is evaluated by two methods. One is based on the pressure angle under the assumption of point contact. The other is measured by the virtual coefficient of screw theory. Comparisons of the two results are studied. An optimization is conducted to minimize sliding velocity and maximize the transmission performance simultaneously. Results show that the kinematic characteristic of the mechanism has been improved.

Optimal dynamic design of anthropomorphic robot module with redundant actuators

In this paper, a study on the optimal dynamic design for an anthropomorphic robot module with redundant actuators is performed. Musculoskeletal structure of human body is a typical example of redundantly actuated mechanism, and provides superior features than general robotic mechanisms. An anthropomorphic robot module that resembles the structure of human upper limb is introduced to utilize the advantages of redundant actuation system. Optimal dynamic design of the proposed robot module that follows optimal kinematic design is carried out to maximize the advantages. Five design indices are introduced, which are associated with inertia matrix, inertia power array representing nonlinear terms and gravity terms of the dynamic modeling equation. A concept of composite design index based on max-min principle of fuzzy theory is employed to deal with multi-criteria based design. As a result of dynamic optimization, a set of dynamic parameters, representing optimal mass distribution of the manipulator is obtaind. It is shown that the dynamic optimization yields a notable enhancement in dynamic performances, as compared to the case of kinematic optimization only.

Kinematic Isotropy and Optimal Kinematic Design of Planar Manipulators and a 3-DOF Spatial Manipulator

Robot operation near isotropic configurations, in which the condition number of the Jacobian matrix reaches unity, is desirable from several points of view. However, determination of all such configurations, given arbitrary robot geometry, is a rather complex problem. In this article all the isotropic configurations of planar manipulators with two, three, and four degrees of freedom are determined, together with that of a 3- DOF spatial manipulator. The solutions are obtained in the form of a fourth-order polynomial for the 3-DOF robot and an eighth-order polynomial for the 4-DOF planar manipulator, resulting in a maximum of eight sets of solutions. The condition numbers are obtained as explicit analytic functions of joint coordinates and link lengths ratios. The optimal length of the links is determined by minimizing the criterion that the condition number increase most slowly with joint angles in the vicinity of isotropic configurations.

Singularity analysis and representation of planar parallel manipulators

In this paper, analytical expressions describing the singularity loci of simple planar three-degree-of-freedom parallel manipulators are derived. They are obtained using the analytical form of the Jacobian matrix, which is known to be singular when the manipulator is in a degenerate configuration. The expressions derived are then used to superimpose graphical representations of the manipulators' singularity loci and workspace. Both types of local degeneracies that can occur for parallel manipulators are studied. However, architecture singularities, which are rather trivial for the type of manipulators studied here, are assumed to be avoided by a proper choice of the manipulator's kinematic parameters. It is shown that, given certain assumptions on the geometry and for a given orientation of the end-effector, the singularity locus in the ( x, y) plane will always be a hyperbola. Moreover, when the passive revolute joints on the base and on the platform are respectively placed symmetrically, the hyperbola degenerates into a straight line. All these results are illustrated with examples of planar parallel manipulators. Some cases for which the singularities are located outside of the workspace are also presented. The analytic description of the singularity loci of manipulators in the Cartesian space can be used for analysis and optimum kinematic design. The expressions derived here have been integrated in a CAD package for parallel manipulators which provides a quick graphical representation of the singularity loci.

Optimal Design of Traction Drive Continuously Variable Transmissions

An optimal design technique for minimum power loss in traction drive continuously variable transmissions is developed. The general forms of the objective function and constraint equations are derived, and the formulated optimal design problems are implemented in a nonlinear programming algorithm. Kinematic analysis and optimal design problem formulation are performed for a selected traction drive configuration as an example of the procedures.

The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator

In this paper, the design of a spherical three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Three different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) workspace maximization, and (c) isotropy. The associated problems are formulated and their solutions, one of them requiring to resort to a numerical method, are provided. Optimum designs are thereby obtained. A discussion on singularities is also included.

Optimal Kinematic Design of 6R Manipulators

A fundamental theorem for the kinematic design of robot manipulators is formulated and proved. Roughly speaking, the theorem states that a manipulator having six revolute joints is optimal if and only if the manipulator or its kine matic inverse is an elbow manipulator. By "optimal" we mean a manipulator that has the properties of (i) maximal work-volume subject to a constraint on its length and (ii) well-connected workspace—that is, the ability to reach all positions in its workspace in each configuration. The notion of work-volume we use is that derived from the translation- invariant volume form on the group of rigid motions. This notion of volume is intermediate between those of "reach able" and "dextrous" workspace and appears to be more natural in that it leads to simple analytical results.

The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator

In this paper, the design of a planar three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Four different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) the existence of a nonvanishing workspace for every orientation of the gripper (c) the maximization of the global workspace, and (d) the isotropy of the Jacobian of the manipulator. The four associated problems are formulated and their solutions are derived. Two of these require to resort to numerical methods for nonlinear algebraic systems. Results of optimum designs are also included.

Integrated Kinematic and Dynamic Optimal Design of Flexible Planar Mechanisms

The following describes a new integrated approach to the problem of designing high speed mechanisms. Employing a nonlinear programming formulation, it allows both the kinematic parameters and the link cross sections to vary while simultaneously bounding trajectory accuracy and minimizing the disturbing force on the ground. Furthermore, link stresses are bounded to limits imposed by the designer. The technique is capable of taking into account the complex coupling which exists between kinematic and dynamic characteristics in flexible mechanisms to determine linkage parameters which best satisfy a given set of design requirements. A path synthesis problem is used to illustrate the technique.

Kineto-elastodynamic balancing of 4R-four bar mechanisms combining kinematic and dynamic stress considerations

When a mechanism runs at high speed and has elastic links, its links vibrate under the action of forces present on the mechanism. The acceleration field resulting from the vibration of the links develops additional interia forces called kineto-elastodynamic (KED) inertia forces. The present paper takes into account the contribution of the KED inertia forces towards the shaking force and shaking moment while balancing planar mechanisms. Combining kinematic design and dynamic stress considerations an optimal kinematic design of the mechanism satisfying the given aim and optimal cross-sectional areas of the links were determined such that the shaking force trasmitted to the foundations due to the combined effect of rigid-body inertia forces and KED inertia forces is a minimum.

Optimum kinematic design of machine tool gear boxes

Published work on computer aided kinematic design of machine tool gear boxes has been limited to normal & overlapping structures only, using a single criterion, such as minimum number of gears, minimum weight etc. for selecting the optimum layout. This paper presnets a comprehensive methodology for optimum kinematic design of machine tool gear boxes, using a multiple criterion optimising approach. A computer program in FORTRAN-IV has been developed to provide the optimum layout version for normal and all types of special structures. The CPU time is 5 sec. The program has been checked by case study of 3 existing machines.