Delun Wang

Orientation and Workspace Analysis of the Multifingered Metamorphic Hand—Metahand

This paper introduces for the first time a metamorphic palm and presents a novel multifingered hand, known as Matahand, with a foldable and flexible palm that makes the hand adaptable and reconfigurable. The orientation and pose of the new robotic hand are enhanced by additional motion of the palm, and workspace of the robotic fingers is complemented with the palm motion. To analyze this enhanced workspace, this paper introduces finger-orientation planes to relate the finger orientation to palm various configurations. Normals of these orientation planes are used to construct a Gauss map. Adding an additional dimension, a 4-D ruled surface is generated to illustrate orientation and pose change of the hand, and an orientation-pose manifold is developed from the orientation-pose ruled surface. The orientation and workspace analysis are further developed by introducing a triangular palm workspace that evolves into a helical surface and is further developed into a 4-D representation. Simulations are presented to illustrate the characteristics of this new dexterous hand.

Biological Modeling and Evolution Based Synthesis of Metamorphic Mechanisms

A methodology for synthesis and configuration design of metamorphic mechanisms is developed in this paper based on biological modeling and genetic evolution with biological building blocks. The goal is to conceive an appropriate source-metamorphic-mechanism configuration when the multiple phases of kinematic functions are given. The key enabler is the way of developing genetic evolution in modeling and design by capturing the metamorphic configuration characteristics. With the unique characteristic of achieving multiple working-phase functions in a mechanism, the metamorphic mechanism possesses two features: one, the ametabolic feature referring to the specified working phases that can be accomplished by a number of traditional mechanisms; two, the metamorphic feature occurring in transition between different working phases, resulting in change of topology of the mechanism. Based on this transition between phases, the concept of mechanism evolution is for the first time introduced in this paper based on biological building blocks in the form of metamorphic cells and associated intrinsic elements as the metamorphic gene. This leads to development of cell evolution and genetic aggregation with mechanism decomposition and evolutionary operation based on mapping from the source-metamorphic mechanism to multiphase working configurations. Examples are given to demonstrate the concept and principles.

Geometric Analysis and Synthesis of the Metamorphic Robotic Hand

This paper presents a novel robotic hand with a metamorphic palm which changes the traditional structure of a robotic hand. Based on this new hand structure, the paper investigates motion of the robotic fingers with respect to the palm by presenting finger operation planes and by revealing the relationship between finger motion and palm motion. The study presents the normals of the finger operation planes as a function of the input angles of the palm and uses these normals to relate finger motion to palm motion. This leads to the coaxial condition of the finger-palm relationship that is then converted to the coplanar condition of normals of all finger operation planes. The condition is then used to generate a coupler trajectory, and the iterative trajectory fitting and curve approximation are used for synthesis of palm links, leading to differential geometry based synthesis of angular lengths of the metamorphic palm.

Kinematic Fundamentals of Planar Harmonic Drives

This paper presents the kinematic model and offers a rigorous analysis and description of the kinematics of planar harmonic drives. In order to reflect the fundamental kinematic principle of harmonic drives, the flexspline of a harmonic drive is assumed to be a ring without a cup. A tooth on the flexspline is a rigid body, and the motion of the tooth is fully governed by the wave generator and the nominal transmission ratio of the harmonic drive. The proposed model depicts the flexspline tooth and the wave generator as a cam-follower mechanism, with the follower executing a combined translating and oscillating motion. With the rigid tooth motion obtained, the conjugate condition between the flexspline and the circular spline is determined, from which the conjugate tooth profile can be derived. In this paper, the motion is governed by geometry, and the flexibility of the flexspline only serves as a spring to maintain the contact between the cam and the follower. For any wave generator and any transmission ratio, the explicit expression of the conjugate condition is presented. For a given circular or flexspline tooth profile, the exact conjugate tooth profile can be obtained. The phenomenon of twice engagement is discussed for the first time.

Kinematic Geometry of Circular Surfaces With a Fixed Radius Based on Euclidean Invariants

A circular surface with a fixed radius can be swept out by moving a circle with its center following a curve, which acts as the spine curve. Based on a system of Euclidean invariants, the paper identifies those circular surfaces taking lines of curvature as generating circles and further explores the properties of the principal curvatures and Gaussian curvature of the tangent circular surfaces. The paper then applies the study to mechanism analysis by proving the necessary and sufficient condition for a circular surface to be generated by a serially connected C′R, HR, or RR mechanism, where C′ joint can be visualized as a special H joint with a variable pitch of one degree of freedom. Following the analysis, this paper reveals for the first time the relationship between the invariants of a circular surface and the commonly used D-H parameters of C′R, HR, and RR mechanisms.

Kinematic geometry for the saddle line fitting of planar discrete positions

The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.

Pre-deformation for assembly performance of machine centers

The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the effect of machine center elastic deformations on workspace volume. Therefore, a method called pre-deformation for assembly performance is presented. This method is technically based on the characteristics of machine tool assembly and collaborative computer-aided engineering (CAE) analysis. The research goal is to enhance assembly performance, including straightness, positioning, and angular errors, to realize the precision of the machine tool design. A vertical machine center is taken as an example to illustrate the proposed method. The concept of travel error is defined to obtain the law of the guide surface. The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre-deformation. Then, the guide surface in normal direction is processed with the pre-deformation function, and the machine tool assembly performance is measured using a laser interferometer. The measuring results show that the straightness deviation of the Z component in the Y-direction is 158.9% of the allowable value primarily because of the gravity of the spindle head, and the straightness of the X and Y components is minimal. When the machine tool is processed in pre-deformation, the straightness of the Z axis moving component is reduced to 91.2%. This research proposes a pre-deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers.

Differential Contact Path and Conjugate Properties of Planar Gearing Transmission

This paper presents a general conjugation model based on the intrinsic kinematical properties of the contact path. The model is truly general for any planar transmission through contact curves, such as gearing. The effectiveness of the method is not affected by the type of centrodes or motion and path of contact. With the method, for any given centrodes and any chosen path of contact, the corresponding conjugate curves can be identified and the geometric properties of the conjugation can be determined even before the conjugate curves are found. The method is demonstrated with straight, circular, and polynomial paths of contact in both circular and noncircular gears. The versatility of the theory and the outstanding features of the method become obvious with treating arbitrary centrodes or any planar motion transmission. The freedom of selecting contact path suggests the possibility of optimal conjugation design.

Characteristic Matrices and Conceptual Design of Hydraulic Systems

The paper presents a new conceptual design method that is capable of generating large numbers of possible design concepts of hydraulic systems automatically for specified operation requirements. A hydraulic system is regarded as a set of single-action subsystems and each subsystem is formed by a set of basic transformation units representing hydraulic components and their usage patterns. The input and output energy characteristic states of a subsystem or basic transformation unit are represented by qualitative vectors related by a diagonal characteristic matrix. Each element of the matrix defines a simple transformation and the operation rules of these transformations are defined. The subsystem characteristic matrix is the product of the characteristic matrices of the basic transformation units. The characteristic matrices of all basic transformation units are identified and classified and the decomposition rules for subsystem characteristic matrices are established. Thus, the characteristic matrix of a subsystem can be successively decomposed into various sets of characteristic matrices of basic transformation units. Each set of such basic transformation units is the topological representation of a hydraulic system. By successive decomposition of a system characteristic matrix, a thorough conceptual design process for hydraulic systems is established. The proposed method is illustrated by examples.

Elastic Kinematic and Geometric Model of Harmonic Gear Drives

The paper presents the first elastic meshing law and spatial elastic conjugation tooth profile for harmonic gear drives. The kinematics and geometry of harmonic drives that have a cup-type flexible spline with an oval wave generator is investigated. The deformation function of the neutral layer of a flexspline is investigated and calculation example is taken by non-linear finite element software. The mathematic model of kinematics of harmonic drive is set up, in which the spatial deformation of a flexspline is separated into a set of deformed curves on the cross sections vertical to the axis. Thus, the spatial engagement in harmonic drive can be visualized as a set of planar engagement. The properties of the instant center and the centrodes of the flexspline tooth relative to the circular spline are studied. The phenomenon of twice engagement at one tooth point of circular spline is found for the first time. The planar gearing engagement and the instant center equation are analyzed and a vigorous spatial elastic conjugation theory is provided for harmonic gear drive.Copyright