This paper addresses an optimal planning problem for workpiece localization with coordinate measurements. The fundamental issue is to find the best probing locations and a suitable sampling size, such that the uncertainty of the localization error is within a predefined limited bound. First, we introduce two sequential optimization algorithms to incrementally increase the localization accuracy, defined by the determinant of the information matrix of the measurements. Then, a reliability analysis method is incorporated for finding a sample size that is sufficient to reduce the uncertainty of the localization error to a limited bound. By combining these two analysis tools, we present a near-optimal probing strategy for finding the best probing locations and a suitable sampling size. With this strategy, given the desired translation and orientation error bounds and desired confidence limit, we can experimentally determine the least number of points needed to measure. Simulation and experimental results show the efficiency of the proposed probing strategy.

This paper presents an optimal planning problem for workpiece measurement. Two sequential optimization algorithms are introduced to find maximum determinant solutions. Then, based on a reliability analysis of workpiece localization and the sequential optimization algorithms, a computer-aided probing strategy is proposed. With this strategy, given the desired translation and orientation error bounds and desired confidence limit, we can experimentally find the least number of points needed to measure. Simulation results show the efficiency of the computer-aided probing strategy.

Workpiece localization has many applications in manufacturing automation. Symmetric localization plays an important role in it, since many commonly used features in engineering design are symmetric. We discuss some new found problems in symmetric localization. We find that multiple solutions exist even for localizing a cube, for which it was known that a unique solution should be found before. Then, we re-explore the symmetry subspaces for symmetric features. After that, we find that some symmetric features have different configuration spaces as known before. This is actually the cause of the problem. A symmetric localization algorithm and simulation results are given to fix the existing problems.

Workpiece localization has direct relations with many manufacturing automation applications. In order to gain accurate workpiece measurement by coordinate measuring machines (CMM) or on-machine measurement system, the touch trigger probe is widely adopted. In spite of the high repeatability of the touch trigger probe, there are still error sources associated with the probe. In this paper, we will focus on probe radius compensation. Several compensation methods in related papers are reviewed. In addition, a new radius compensation method is proposed in this paper. Simulation and experimental results of probe radius compensation by different methods are given. It is shown that our proposed method has the best performance both in terms of compensation accuracy and computational time. The method is also implemented in a computer aided setup (CAS) system.

Studies the dynamics of parallel manipulators. We first have a brief review and discussion on different dynamics formulations in the literature (Newton-Euler, direct Lagrangian, and Lagrange-D'Alembert formulation on the reduced system). Then we show the equivalence of these methods. Based on the concepts from differential manifolds, we prove that away from configuration singularity, there exists a projection from the joint space to parameterize the configuration space. The fact that the dynamics is well defined even at actuators singularity, end-effector singularity and other kinds of parameterization singularity is highlighted. For the method of reduced systems, there are two main drawbacks. Firstly the joints being cut for forming the tree system are presumed to have no external torque. Secondly the force and torque applied to other links of the manipulator is not considered. We propose two methods to remedy the situation. Firstly by cutting a link instead of a joint, all the joints torque can be incorporated into our equations of motion. This is useful not only for the case of actuating all the joints, but also if we consider compensating the joints friction. Secondly we propose a concept of transforming force to the generalized force space so that all the other forces and torque can be considered.

Parallel manipulators with redundant actuation present both problems and advantages. We analyze some major advantages of redundancy to demonstrate its usefulness. The dynamics of closed-chain mechanisms has been studied by many researchers. However, they often only consider the case of normal actuation. Few methods are suitable for closed-chain mechanisms with redundant actuation. In the article, the dynamic model of redundantly actuated closed-chain mechanisms is presented explicitly by applying Lagrange-D'Alembert formulations. As an illustrative example, the dynamic model of a 2-DOF planar parallel redundant manipulator is presented. A PID control algorithm in the joint space is experimentally implemented on this parallel manipulator to perform trajectory tracking. The experimental results show the validity of PID control.

Singularity is a fundamental problem in the analysis of parallel mechanisms. The distribution of singularity in the workspace will determine to a great extent the properties of parallel mechanisms. We study the distribution of actuator singularity, which can also be applied to analyze end-effector singularity. A very important observation has been made that these two kinds of singularities are caused by the parameterization of a configuration manifold by actuator coordinates or end-effector coordinates. Despite the various styles of singularities of parallel mechanisms, there are some rules which govern the behavior of stable singularities. These rules provide some useful ideas in the design of redundant parallel mechanisms so as to achieve better performance in high speed motion and improve their stiffness. Optimal kinematic and dynamic control algorithms are designed and implemented which make use of the redundancy of the parallel mechanism. Experimental results agree with our expectation.

Workpiece localization and similar problems have attracted many researcher in robotics, computer vision and image processing research fields. Workpiece localization algorithms have close relations with workpiece setup in manufacturing process. However when these algorithms apply to a computer aided setup (CAS) system, many problems, like online measurement planning and error compensation etc., should be solved first. In this paper, a CAD model based CAS system will be introduced. This system is based on an open architecture CNC machine. Some problems in implementation are also addressed, such as algorithm divergence. The system has used a new method to avoid the possible divergence of localization algorithms. New error compensation method has been applied in the localization algorithms, instead of directly compensating the measurement data. Experimental results will be given to show the effect of these new methods and the efficiency of the CAS system.

A datum reference frame (DRF) is a coordinate system used to locate and orient part features. Constructing a DRF from a set of datum features is a complicated process involving: a) specifying a valid combination and the precedence of the datum features which define the DRF; b) developing datum from datum features of the part; and c) determining the position and orientation of the DRF from the datums. We develop a geometric theory for establishing DRFs. The theory is based on the observation that a datum feature such as a plane, a cylinder or a sphere has a symmetry subgroup G/sub 0/ under the action by the group SE(3) of rigid motions in R/sup 3/. Thus, the configuration space of a datum feature can be identified with the homogeneous space SE(3)/G/sub 0/, and the problem of datum development can be posed as a minimization problem in SE(J)/G/sub 0/. We give conditions under which a datum feature qualifies to be a secondary or a tertiary datum. We present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem in the homogeneous spaces of SE(3). We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach.