In this paper, we present an experimental evaluation of the Cartesian stiffness of a novel parallel wrist under redundant and antagonistic actuation. The mechanism in consideration is Omni-Wrist V (OW5), a two degrees-of-freedom (DoF) parallel mechanism redundantly actuated by three subchains. We first give a brief review of its kineto-statics and derive its reduced Cartesian stiffness model. To illustrate the stiffness enhancement of OW5 under redundant and antagonistic actuation, its Cartesian stiffness is measured and evaluated under four control schemes: the non-redundant control, the minimum 2-norm torque control without or with redundant encoder, and the antagonistic actuation control. Measurement data are represented using stiffness matrices and stiffness ellipses. Our study offers a quick quantitative evaluation of stiffness enhancement of OW5 under redundant and antagonistic actuation.

Due to the effect of joint clearance and component flexibility ( joint or link), a parallel kinematic manipulator (PKM), with proposed motion type G ⊂ SE(3), may have undesirable (or uncompensatible) pose error beyond G at the end-effector, which would cause severe accuracy performance degeneration of the PKM. As such phenomenons have been discovered and verified in many researches, we proposed a new performance index, called “Type Error”, which could be applied to evaluate such undesirable errors. Specifically with this index, the largest translational/rotational pose error could be quantized and the worst case over the designed workspace can be predicted. A three-step method for general application is presented in details by case study of three kinds of translational PKM.

In this paper, we identify a class of structurally distinguished machines, called quotient kinematics machines (QKM). A QKM realizes a motion task, typically characterized by a subgroup G of rigid transformation group SE(3), through coordinated motion of two mechanisms called modules. One is referred to as a subgroup module H and the other a complementary or quotient module G/H of H in G. Since QKM can retain both large workspace/rotation range of SKMs and speed/accuracy of PKMs by appropriate choice of modules, it is often implemented in high end machine design for semiconductor die/wire-bonding and 5-axis machining, etc. To promote QKM technology beyond occasional studies and applications, we use differential geometric techniques to develop a rigorous and precise treatment of QKMs, including: (i) modeling and analysis of QKMs; (ii) classification and synthesis of QKMs; (iii) PKM realization of quotient modules.

The advantages of tilt-and-torsion angles in analysis of zero-torsion parallel kinematics machines (PKM) have been reported by several literatures. However, geometric properties of tilt-and-torsion angles are not completely understood and fully utilized in synthesis of novel zero-torsion PKMs. In this paper, we study geometric properties of the so called zero-torsion motion types via differential geometry of Lie groups. We show that zero-torsion motion types admit simple representations under canonical coordinates of the first kind of the special Euclidean group SE(3). Using the proposed representation, we give a classification of zero-torsion PKMs. The synthesis condition for several well known zero-torsion PKMs are correctly identified. We will conduct type synthesis of zero-torsion PKMs in a separate paper.

In view of the successful application of planar parallelogram in the Delta robot and its variants, we are interested to investigate mechanisms consisting of spatial parallelograms. The spatial parallelogram, denoted by Pscra*, is a 2-SS (S stands for a spherical joint) parallel mechanism having identical length for opposite links. We show that a 3-PPscra* mechanism is generically undergoes 3-dimensional purely translational motion. Based on the 3-PPscra* topology, an integrated optimal design on both architecture and geometry design is carried out. Using the formulation of maximizing effective cubic workspace, the Orthopod, which has three orthogonally arranged linear joint axes, is found to be the best in our settings. A prototype machine of the Orthopod is thus designed and manufactured.