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.

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.

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.

The paper and its companion [Dong et al., 2011, “Kinematic Fundamentals of Planar Harmonic Drives,” ASME J. Mech. Des., 133(1), p. 011007], which treats a harmonic drive without a cup, present the geometry-relevant operation of harmonic drives under an ideal little or no-load condition. This paper shows that the cup is essentially a compliant mechanism with the unique feature of transforming a set of different tooth rotations into a single rigid body rotation and demonstrates how the cup affects tooth conjugation and the conjugate tooth profiles. It proves and demonstrates that the conjugating tooth profile should be a three-dimensional surface because of the cup deformation. The use of spur gears on both flexspline and circular spline will cause excessive interference and excessive deformation will become necessary to overcome the interference. Since no-load geometry is clearly identified, excessive deformation and errors due to incorrect geometry can be removed or filtered and the loading effects can be identified. Contact ratio of a harmonic drive is also obtained through the range of conjugate positions. Although loading is not considered, the geometric error is. Eliminating or reducing geometric error will improve the performance.

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.

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