Sliding–Rolling Contact and In-Hand Manipulation

The following sections are included:

• Dedication
• Preface
• About the Authors
• Contents

The following sections are included:

• A Brief History of Rolling–Sliding Contact and In-Hand Manipulation
• Outline of the Book
  • Statement of the Problem
  • Aims and Objectives
• Organization of the Book

In this chapter, we introduce the moving-frame method to study the differential properties of curves and surfaces. In particular, we obtain the infinitesimal displacement of the Frenet frame on a spatial curve in terms of curvature k and torsion τ and then the infinitesimal displacement of the Darboux frame on a surface curve in terms of geodesic curvature k_g, normal curvature k_n, and geodesic torsion τ_g.

In this chapter, we introduce the adjoint approach, which is a powerful tool to study kinematic differential geometry when two geometric entities, such as curves and surfaces are present. The basic idea is to observe the changes of one entity while the observer moves with the moving frame of the other entity.

In this chapter, we develop the forward kinematics of two rigid surfaces with rolling contact when the contact trajectory on each surface is present. We use the moving-frame method and the adjoint approach to obtain the instantaneous forward kinematics in terms of geometric invariants: rolling rate, normal curvature, geodesic curvature, and geodesic torsion. This approach is coordinate-invariant in the sense that the equations are invariant w.r.t. the Special Euclidean group in ℝ³.

In this chapter, we extend the approach presented in Chapter 4 to rolling–sliding contact: the moving surface rolls and slides simultaneously on the fixed surface. We derive both the angular velocity and translational velocity of the moving surface when the two contact trajectories are present.

In this chapter, we consider two surfaces subject to rolling contact and obtain the contact trajectories when the angular velocity of the moving surface is present. We obtain three scalar entities that generate the contact trajectories to realize the given angular velocity of the moving surface: the rolling direction φ, the rolling rate σ, and the complementary spin rate ω_spin.

In this chapter, we extend the approach presented in Chapter 6 to rolling–sliding contact: the moving surface rolls and slides simultaneously on the fixed surface. We obtain the contact trajectories when the translational velocity and rotational velocity of the moving surface are given. We obtain five scalar entities: the sliding rate ρ, sliding direction δ, rolling direction φ, the rolling rate σ, and the complementary spin rate ω_spin. These five entities generate the contact trajectories to realize the given angular velocity and translational velocity of the moving surface.

The Metahand—metamorphic robotic hand—was developed based on the concept of metamorphosis stemming from origami folding at King’s College London [Dai et al., 2009; Cui and Dai, 2012; Cui et al., 2017]. Different from other robotic hands, The Metahand has an articulated palm formed by a spherical linkage, enabling the palm to change mobility, topology, and configuration. The Metahand is capable of emulating more sophisticated grasping and dexterous manipulation. It also allows the robotic hand to be fully folded to pass through tight spaces and to be redeployed to adapt for various task requirements…

In this chapter, we investigate the workspace of the articulated palm and the posture workspace of the Metahand.We apply the concept of Gauss map to the finger-operation plane and visualize the triangular palm workspace and helical posture workspace.

In this chapter, we incorporate the kinematic formulations of rolling contact and in-hand manipulation with fixed-point contact developed in previous chapters into that of in-hand manipulation with rolling contact. The proposed formulation admits a high degree of coordinate independence.

The following sections are included:

• Appendix
• Bibliography
• Index