Dimensional Synthesis of a Novel 3-URU Translational Manipulator Implemented through a Novel Method

A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians’ properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists).

Kinematics of a 6-DOF parallel manipulator with two limbs actuated by spherical motion generators

Inspired by dual-arm-like manipulation, a novel 6-DOF parallel manipulator with two spherical-universal-revolute limbs is proposed. Compared with general 6-DOF parallel manipulators with six limbs, this new manipulator actuated by spherical motion generators has only two limbs, which brings advantages such as fewer active limbs for avoiding interference, larger reachable and orientational workspace for complex operating, more actuators integrated in active modules for decreasing installation errors and increasing compactness. In this paper, the kinematics of this novel parallel manipulator is solved and illustrated, covering its inverse and forward position analysis, workspace and singularities. The kinematic study reveals interesting features of this manipulator such as multiple working and assembly modes, small footprint and large workspace volume with high dexterity. Numerical examples of kinematic analysis are included. Practical application of the new manipulator is illustrated.

A geometrical formulation for the workspace of parallel manipulators

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

A Constraint-Based Approach to Manipulator Kinematics and Singularities

<p>In this thesis, a differential-geometric approach to the kinematics of multibody mechanisms is introduced that enables analysis of singularities of both serial and parallel manipulators in a flexible and complete way. Existing approaches such as those of Gosselin and Angeles [1], Zlatanov et al. [2] and Park and Kim [3] make use of a combination of joint freedoms and constraints and so build in assumptions. In contrast, this new approach is solely constraint-based, avoiding some of the shortcomings of these earlier theories. The proposed representation has two core ingredients. First, it avoids direct reference to the choice of inputs and their associated joint freedoms and instead focuses on a kinematic constraint map (KCM), defined by the constraints imposed by all joints and not requiring consideration of closure conditions arising from closed loops in the design. The KCM is expressed in terms of pose (i.e. position and orientation) variables, which are the coordinates of all the manipulator’s links with respect to a reference frame. The kinematics of a given manipulator can be described by means of this representation, locally and globally. Also, for a family of manipulators defined by a specific architecture, the KCM will tell us how the choice of design parameters (e.g. link lengths) affects these kinematic properties within the family. At a global level, the KCM determines a subset in the space of all pose variables, known as the configuration space (C-space) of the manipulator, whose topology may vary across the set of design parameters. The Jacobian (matrix of first-order partial derivatives) of the KCM may become singular at some specific choices of pose variables. These conditions express a subset called the singular set of the C-space. It is shown that if a family of manipulators, parametrised by a manifold Rd of design parameters, is “well-behaved” then the pose variables can be eliminated from the KCM equations together with the conditions for singularities, to give conditions in terms of design parameters, that define a hypersurface in Rd of manipulators in the class that exhibit C-space singularities. These are referred to as Grashof-type conditions, as they generalise classically known inequalities classifying planar 4-bar mechanisms due to Grashof [4]. Secondly, we develop the theory to incorporate actuator space (A-space) and workspace (W-space), based on a choice of actuated joints or inputs and on the manipulator’s end-effector workspace or outputs. This will facilitate us with a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s C-space. This provides new insight into the structure of the forward and inverse kinematics, especially for parallel manipulators. The theory is illustrated by a number of applications, some of which recapitulate classical or known results and some of which are new.</p>

A Constraint-Based Approach to Manipulator Kinematics and Singularities

<p>In this thesis, a differential-geometric approach to the kinematics of multibody mechanisms is introduced that enables analysis of singularities of both serial and parallel manipulators in a flexible and complete way. Existing approaches such as those of Gosselin and Angeles [1], Zlatanov et al. [2] and Park and Kim [3] make use of a combination of joint freedoms and constraints and so build in assumptions. In contrast, this new approach is solely constraint-based, avoiding some of the shortcomings of these earlier theories. The proposed representation has two core ingredients. First, it avoids direct reference to the choice of inputs and their associated joint freedoms and instead focuses on a kinematic constraint map (KCM), defined by the constraints imposed by all joints and not requiring consideration of closure conditions arising from closed loops in the design. The KCM is expressed in terms of pose (i.e. position and orientation) variables, which are the coordinates of all the manipulator’s links with respect to a reference frame. The kinematics of a given manipulator can be described by means of this representation, locally and globally. Also, for a family of manipulators defined by a specific architecture, the KCM will tell us how the choice of design parameters (e.g. link lengths) affects these kinematic properties within the family. At a global level, the KCM determines a subset in the space of all pose variables, known as the configuration space (C-space) of the manipulator, whose topology may vary across the set of design parameters. The Jacobian (matrix of first-order partial derivatives) of the KCM may become singular at some specific choices of pose variables. These conditions express a subset called the singular set of the C-space. It is shown that if a family of manipulators, parametrised by a manifold Rd of design parameters, is “well-behaved” then the pose variables can be eliminated from the KCM equations together with the conditions for singularities, to give conditions in terms of design parameters, that define a hypersurface in Rd of manipulators in the class that exhibit C-space singularities. These are referred to as Grashof-type conditions, as they generalise classically known inequalities classifying planar 4-bar mechanisms due to Grashof [4]. Secondly, we develop the theory to incorporate actuator space (A-space) and workspace (W-space), based on a choice of actuated joints or inputs and on the manipulator’s end-effector workspace or outputs. This will facilitate us with a framework for analysing singularities for forward and inverse kinematics via input and output mappings defined on the manipulator’s C-space. This provides new insight into the structure of the forward and inverse kinematics, especially for parallel manipulators. The theory is illustrated by a number of applications, some of which recapitulate classical or known results and some of which are new.</p>