Jian Meng

A Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators

Mechanism synthesis is mostly dependent on the designers experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.

Accuracy Analysis of Parallel Manipulators With Joint Clearance

Due to joint clearance, a parallel manipulators end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or non-overconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Auto-calibration for a parallel manipulator with sensor redundancy

In this paper, we propose two algorithms for the auto-calibration of the home position or the joint angle offsets for a parallel manipulator by utilizing the extra sensor(s) information (sensor redundancy), sampling over the workspace, and optimizing a suitably chosen cost function, without resorting to any other external equipment. Meanwhile, a measure or estimate of the precision of the machine is also obtained. It is very useful and convenient if the machine needs frequent re-calibration. Simulations and experiments are also performed to show the effectiveness of the algorithms.

A Geometric Theory for Synthesis and Analysis of Sub-6 DoF Parallel Manipulators

This paper presents a rigorous and precise geometric theory for the analysis and synthesis of sub-6 DoF parallel manipulators. We give a rigorous definition for the parallel manipulator synthesis problem, and introduce a general method for specifying the corresponding subchains which will result in the desired parallel manipulator. Following this, a procedure for solving the parallel manipulator synthesis problem is proposed when the set of desired end-effector motions is in the form of Lie subgroup or a regular submanifold of SE(3). Numerous examples are used to illustrate the generality and effectiveness of the proposed synthesis method.

A general approach for accuracy analysis of parallel manipulators with joint clearance

Due to the joint clearance, parallel manipulators always exhibit some position and orientation errors at the mobile platform. This paper aims to present a novel and general approach for evaluating the maximal pose deviation of the mobile platform under the influence of joint clearance. First, it shows and proves that overconstrained parallel manipulators can not work without clearance. Then, an efficient method is proposed to evaluate the maximal pose errors for general spatial parallel manipulators with joint clearance. A numerical example shows the application and efficiency of the proposed approach.

Accuracy Analysis of General Parallel Manipulators with Joint Clearance

Due to the joint clearance, parallel manipulators always exhibit some position and orientation errors at the mobile platform. This paper aims to provide a systematic framework for the error analysis problem of general parallel mechanisms influenced by the joint clearance. A novel and efficient method is proposed to evaluate the maximal pose errors of general spatial parallel manipulators with joint clearance.

Assembly Problem of Overconstrained and Clearance-free Parallel Manipulators

To avoid deteriorating the mechanisms performance, joint clearance can be eliminated by preloading the pairing elements of the joint. However, this paper proves rigorously that in the real world, the unavoidable assembly and manufacturing errors will cause overconstrained parallel manipulators to lose degree of freedoms, or even unable to be assembled if they are composed of purely clearance-free pairs (e.g., preloaded pairs). Introducing joint clearance is an essential and efficient way for the correct functioning and easy assembly of overconstrained parallel manipulators.

Finite Motion Validation for Parallel Manipulators: A Differential Geometry Approach

Type synthesis of low (3-5) degree of freedom (Dof) spatial parallel manipulators is well documented in literature. Recent approaches such as proposed in J.M. Herve and F. Sparacino (1991) - Z. Huang and Q.C. Li (2003) showed some systematic design capability, but did not develop an equally effective means to check for prescribed finite motion. In this paper, we studied the finite motion set of parallel manipulators from a general input-affine nonlinear system viewpoint. Differential geometry tools for controllability (reachability) analysis of nonlinear system on a differential manifold are utilized together with lie group theory. Our techniques are shown to be effective by applying to a systematic type synthesis method proposed in M. Jian, et al. (2005) and W. Yuanqing, et al. (2005)

A Geometric Theory for Synthesis and Analysis of Sub-6 DoF Serial Manipulator Subchains

Motivated by the work of Herve and his coworkers, this paper presents a rigorous and precise geometric theory for the synthesis and analysis of sub-6 DoF serial manipulator subchains. First, we review the basic properties of the Special Euclidean group SE(3), Lie subgroups and submanifolds of SE(3). With low dimensional subgroups and submanifolds providing models for the so called primitive generators, the high dimensional subgroups and regular submanifolds provide models for the set of desired end-effector motions. Two important classes of regular submanifolds of SE(3) are studied in detail. Then, starting from a given list of primitive generators, we give a rigorous definition of the synthesis problem for a serial manipulator subchain, and develop a general procedure for solving the synthesis problem when the set of desired end-effector motions is a Lie subgroup or a regular submanifold.

Kinematic synthesis of parallel manipulators: a Lie theoretic approach

This paper provided a unified geometric framework for kinematic analysis and synthesis of parallel manipulators. We gave a strict definition on motion types of a mechanism based on distributions on a Lie group. We derived conditions for parallel manipulators with Lie subgroup motions using the intersection of the permissible velocity spaces, or the direct sum of the constraint force spaces of each subchain, and the integration theory on a Lie group. Several practical examples were studied in detail to verify our approach.