A chronological overview of the applications of control theory to prosthetic hand is presented. The overview focuses on hard computing or control techniques such as multivariable feedback, optimal, nonlinear, adaptive and robust and soft computing or control techniques such as artificial intelligence, neural networks, fuzzy logic, genetic algorithms and on the fusion of hard and soft control techniques. This overview is not intended to be an exhaustive survey on this topic and any omissions of other works is purely unintentional.
This paper uses the exponential defined on a Clifford algebra of planar projective space to show that the “standard-form” design equations used for planar linkage synthesis are obtained directly from the relative kinematics equations of the chain. The relative kinematics equations of a serial chain appear in the matrix exponential formulation of the kinematics equations for a robot. We show that formulating these same equations using a Clifford algebra yields design equations that include the joint variables in a way that is convenient for algebraic manipulation. The result is a single formulation that yields the design equations for planar 2R dyads, 3R triads, and nR single degree-of-freedom coupled serial chains and facilitates the algebraic solution of these equations including the inverse kinematics of the chain. These results link the basic equations of planar linkage design to standard techniques in robotics.
Bennett's linkage is a spatial 4R closed chain that can move with one degree of freedom. The set of relative displacement screws that form the one-dimensional workspace of this device defines a ruled surface known as a cylindroid. The cylindroid is generally obtained as a result of a real linear combination of two screws. Thus, the workspace of Bennett's linkage is directly related to a one-dimensional linear subspace of screws. In this paper, we examine in detail Bennett's linkage and its associated cylindroid, and introduce a reference pyramid which provides a convenient way to relate the two. These results are fundamental to efficient techniques for solving the synthesis equations for spatial RR chains.
Abstract. This paper presents a synthesis procedure for a two-degreeof-freedom spatial RR chain to reach an arbitrary end-effector trajectory. Spatial homogeneous transforms are mapped to 4 x 4 rotations and interpolated as double quaternions. Each set of three spatial positions obtained from the interpolated task is used to define an RR chain. The RR chain that best fits the trajectory is the desired robot. The procedure yields a unique robot independent of the coordinate frame defined for the task.
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