Dexterous Workspace Research Articles

Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator

SUMMARYIn this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

A Family of Kinematically Redundant Planar Parallel Manipulators

Parallel manipulators feature relatively high payload and accuracy capabilities compared to their serial counterparts. However, they suffer from small workspace and low maneuverability. Kinematic redundancy for parallel manipulators can improve both of these characteristics. This paper presents a family of new kinematically redundant planar parallel manipulators with six actuated-joint degrees of freedom based on a 3-PṞRR architecture obtained by adding an active prismatic joint at the base of each limb of the 3-ṞRR manipulator. First, the inverse displacement of the manipulators is explained, then their reachable and dexterous workspaces are obtained. Comparing the proposed redundant manipulators to the original 3-ṞRR nonredundant manipulator, both reachable and dexterous workspaces are substantially larger. Next, the Jacobian matrices of the manipulators are derived, and different types of singularities are analyzed and demonstrated. It is shown that the vast majority of singularities can be avoided by using kinematic redundancy.

Architecture optimisation of three 3- [formula omitted]RS variants for parallel kinematic machining

The 3- P ̲ RS parallel manipulator has recently been prototyped as a machining centre. PRS denotes the prismatic–revolute–spherical architecture of each limb where only the prismatic joint is actuated and hence underlined. Three variations of this manipulator have been independently presented in the literature. The architectural parameters affecting the size of the dexterous workspace volume are identified for each of the three models. The influence of these parameters on each of the three models is studied. Next, the manipulators’ dexterity is defined as the architecture's ability to lend stiffness and accuracy to the machine tool. By studying the singular values and condition number of a newly developed square, dimensionally homogeneous Jacobian matrix, regions of the workspace corresponding to capabilities for high end effector (EE) velocities in each of the degrees of freedom (DOF) are identified. Optimisation of the architectural parameters is then completed to provide the largest possible size for this region. The dexterous workspace size, obtained using optimal architectural parameters unique to each variant, is then compared between each of the three variants of the 3- P ̲ RS manipulator.

Quantitative dexterous workspace comparison of parallel manipulators

Using a novel method for the formulation of Jacobian matrices, this paper quantitatively compares the dexterity of spatial complex degree of freedom parallel manipulators for the first time. The manipulators included in this study are three-degree-of-freedom manipulators including the 3-PRS, 3-RPS, and Tricept. The comparison is made possible through the use of a novel method of formulating square dimensionally homogeneous Jacobian matrices, and a consistent choice of independent end effector velocities. The condition number and singular values of the Jacobians corresponding to each manipulator may then be directly compared. The objective of the work is to illustrate the application of the proposed method in determining the optimal architecture based on predefined operating characteristics.

3-PRRR redundant planar parallel manipulator: Inverse displacement, workspace and singularity analyses

This paper presents a novel configuration for a kinematically redundant planar parallel manipulator . Advantages of redundant versus non-redundant parallel manipulators are first discussed. The inverse displacement problem is examined, and the workspace of the proposed manipulator is compared to that of a similar-sized non-redundant one. It is shown that both the reachable and dexterous workspaces of the redundant manipulator are significantly larger. The Jacobian matrices of the proposed manipulator are then developed, and the direct and inverse singularities , and the combination of both, are presented. The physical interpretation of each type of singularity is discussed and illustrated.

Optimizing the kinematic chains for a spatial parallel manipulator via searching the desired dexterous workspace

This paper exploits a new algorithm to optimize the length of the legs of a spatial parallel manipulator for the purpose of obtaining a desired dexterous workspace rather than the whole reachable workspace. With the analysis of the degree of freedom (DoF) of a manipulator, we can select the least number of variables to depict the kinematic constraints of each leg of a manipulator. The optimum parameters can be obtained by searching the extreme values of the objective functions with the given adroit workspace. Example is utilized to demonstrate the significant advantages of this method in the dexterous workspace synthesis. In applications, this method can be widely used to synthesize, optimize and create all kinds of new spatial parallel manipulator with a desired dexterous workspace.

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity.

Optimum positioning of an underwater intervention robot to maximise workspace manipulability

Underwater robotic vehicles (URV) are extensively used for inspection and intervention tasks of subsea facilities. To enable dexterous manipulations, the URV is required to be firmly attached to the structure. The choice of docking point is very important. An inappropriate choice would necessitate multiple re-dockings. This significantly increases the duration and cost of the mission. In this paper, we present a method of assisting the URV operator to identify the most appropriate docking position in the context of a desired dexterous workspace. The method draws upon classical procedures developed, predominantly, for industrial robotics. Currently, the operator intuitively determines docking positions. A positioning strategy, based on the type of task to be carried out, is proposed. Inspection of a subsea weld joint, using a compact URV and a specially designed and optimised, dexterous, 7 d.o.f., manipulator, is considered as a test case. Dexterity of manipulator at the target location is taken as the optimisation criterion. As a measure of manipulator dexterity, the condition number of the manipulator is adopted here. Manipulator joint limits and workspace constraints are taken into account. Theoretical analysis and simulation results are presented.

Optimization of a planar tendon-driven parallel manipulator for a maximal dextrous workspace

In this article, new methodologies for determining the tension distribution and optimal configurations of planar tendon-driven parallel manipulators (TDPMs) are presented. TDPMs are characterized by the use of cables in place of the linear actuators used in most parallel manipulators. Three separate, but inter-related topics are examined in this article, and methodologies for addressing them are proposed. The first is the determination of cable forces for overconstrained tendon-driven manipulators, which is necessary in order to address the second topic, namely, the development of a methodology for workspace determination of tendon-driven manipulators. The final topic examined is the dimensional synthesis of tendon-driven manipulators for a large dextrous workspace. The numerical methodologies developed here have potential for easy application to more complex spatial cases.

PRIMATE ANATOMY, KINEMATICS, AND PRINCIPLES FOR HUMANOID DESIGN

The primate order of animals is investigated for clues in the design of humanoid robots. The pursuit is directed with a theory that kinematics, musculature, perception, and cognition can be optimized for specific tasks by varying the proportions of limbs, and in particular, the points of branching in kinematic trees such as the primate skeleton. Called the Bifurcated Chain Hypothesis, the theory is that the branching proportions found in humans may be superior to other animals and primates for the tasks of dexterous manipulation and other human specialties. The primate taxa are defined, contemporary primate evolution hypotheses are critiqued, and variations within the order are noted. The kinematic branching points of the torso, limbs and fingers are studied for differences in proportions across the order, and associated with family and genus capabilities and behaviors. The human configuration of a long waist, long neck, and short arms is graded using a kinematic workspace analysis and a set of design axioms for mobile manipulation robots. It scores well. The re-emergence of the human waist, seen in early prosimians and monkeys for arboreal balance, but lost in the terrestrial pongidae, is postulated as benefiting human dexterity. The human combination of an articulated waist and neck will be shown to enable the use of smaller arms, achieving greater regions of workspace dexterity than the larger limbs of gorillas and other hominoidea.

Determination of dexterous workspace of planar 3-DOF parallel manipulator by auxiliary linkages

Determination of dexterous workspace of planar 3-DOF parallel manipulator by auxiliary linkages

Workspace Atlases for the Design of Spherical 3-DOF Serial Wrists

In this paper, the physical model of the solution space of spherical 3-DOF serial wrists is established. The reachable workspaces are classified. The dexterous workspaces for such wrists are investigated based on the rotatability conditions for the spherical 4-bar mechanism. Using the theory of conformal transformation, we obtain plane figures of the reachable and dexterous workspaces. The atlases of the workspaces in the physical model of the solution space are plotted. These results are useful not only for designer overall to understand the relationship between the workspaces and link lengths of spherical 3-DOF serial wrists, but also for the design of the wrists.

Orientation capability of planar manipulators using virtual joint angle analysis

This paper investigates the orientation capability of a serial manipulator by examining the rotatability of its equivalent mechanism and by proposing the workspace region decomposition, based on the polynomial discriminant derived from the virtual angle analysis of the end-effector link of the equivalent mechanism. The range of real number solutions and that of complex number solutions of the virtual angle are characterised using the analysis of the virtual adjustable ground link. The orientation capability is then characterised in a graphical representation which is then mapped onto a new orientation capability map where the partial dexterous workspace and its orientation range with respect to a workspace position are presented in polar coordinates. The study presents a new way of analysing the orientation capability of planar manipulators in terms of orientation boundary loci and orientation maps.

A numerical method for the determination of dextrous workspaces of Gough–Stewart platforms

AbstractAn optimization approach to the computation of the boundaries of different dextrous workspaces of parallel manipulators is presented. A specific dextrous workspace is the region in space in which, at each position of the working point, a manipulator can control the orientation of its upper working platform through a specified range of orientation angles. Here the dextrous workspace is determined from the intersection of suitably chosen fixed orientation workspaces, which are found by application of a constrained optimization algorithm. The procedure is simple and has the considerable advantage that it may easily be automated. The method is illustrated by its application to both a planar and spatial Gough–Stewart platform. Copyright © 2001 John Wiley & Sons, Ltd.

A Mechanism for Dexterous End-Effector Placement During Minimally Invasive Surgery

Presented here is the design of a mechanism for dexterous placement of an end-effector during minimally invasive surgery. A literature review is presented to show that capabilities of the mechanism are unavailable in current instrumentation. Apart from actuation of the end-effector, our mechanism provides 180° bi-directional articulation relative to the support tube and rotation of the end-effector about the articulated axis. These are accomplished via a compact multi-link structure comprised of gears and gear-links that provide excellent stiffness, load capacity and durability. The structure is optimized to have a large and dexterous workspace, low backlash, and small force magnification. Maximization of load capacity and durability of the complete mechanism is achieved by the use of high strength stainless steels, gears with 25° pressure angles to accommodate larger sized teeth, optimized gear pack thicknesses to distribute stresses evenly, and a compact forceps design to reduce tip length. Resistance to pitting is improved by alternating materials and/or hardness of materials between mating parts. The instrument is capable of supporting 4.5 N needle tip loads with infinite life expectancy and loads up to 8.7 N intermittently.

A design procedure for RPR planar robotic workcells: an algebraic approach

A new method is used to determine a satisfactory location of a workpiece in the workspaces of planar RPR robots that can provide dexterous workspace. All three joints, $1, $2, and $3, of the robot have excursion-limits that bound their displacements. For the purpose of this paper, the third joint, a resolute, permits exactly one full turn. The method is to adapt traditional algebraic methods of linkage synthesis to synchronize the available rotation at $3 with the required task-rotations.

A Synthesis Method For Placing Workpieces In RPR Planar Robotic Workcells

A new method is used for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. All three joints of the robot have excursion-limits that bound their displacement. For the purposes of this paper, the third joint, a revolute, permits exactly one full turn. Successful locations for the workpiece are those places where the rotations at each task-axis and the third joint are synchronized. For a fixed mounting angle of the tool, the radial location and orientation of the workpiece are determined by just two 2π-rotations of the tool. When the mounting-angle of the tool is also a variable, the tool can be rotated a full turn at three locations on the workpiece. The method is particularly well suited to applications in which the task requires large rotations of the end-effector. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.

Workspaces of planar parallel manipulators

This paper presents geometrical algorithms for the determination of various workspaces of planar parallel manipulators. Workspaces are defined as regions which can be reached by a reference point C located on the mobile platform. Firts, the constant orientation workspace is determined. This workspace is defined as the region which can be reached by point C when the orientation of the moving platform is kept constant. Then, the maximal workspace, which is defined as the region which can be reached by point C with at least one orientation, is determined. The maximal workspace is also referred to as the reachable workspace. From the above regions, the inclusive workspace, i.e. the region which can be attained by point C with at least one orientation in a given range, can be obtained. Then, the total orientation workspace, i.e. the region which can be reached by point C with every orientation of the platform in a given range, is defined and determined. Finally, the dextrous workspace, which is defined as the region which can be reached by point C with any orientation of the platform, can be determined. Three types of planar parallel manipulators are briefly described and one of them is used to illustrate the algorithms. Each of the workspaces is determined here for this type of manipulator while the derivations for the other types of manipulators will be presented in another paper. The algorithms developed here are useful in the design and motion planning of planar parallel manipulators.

Optimisation of an articulated instrument for enhanced dexterity in minimally invasive therapy

SummaryThe benefits for patients of minimally invasive surgery are reduced trauma, hospitalisation and recovery time. The growth in the number of these procedures is dependent upon the development of articulated tools with enhanced dexterity. In this paper, we examine trends in articulated instrument development and present our own articulated manipulator for minimally invasive surgery (AMMIS). The AMMIS is a single degree-of-freedom compact mechanism, with 180d` bi-directional articulation capability. It can support a surgical tool, exert necessary forces with a moderate driving force and respond quickly. Furthermore, its configuration can be modified and optimised for specific surgical tasks. To this end, we develop criteria for evaluating the optimal performance of articulated tools. These criteria include reachable and dexterous workspaces, force magnification, potential backlash, tip path curvature and maximum articulation angle per link. Using these criteria we outline a procedure for optimisation and determine an optimal AMMIS configuration for the specific task of suturing. A clinician's perspective on the scope and usefulness of AMMIS is presented in the conclusion.

Synthesis and Workspace Study of Endoscopic Extenders With Flexible Stem

Endoscopic surgery is a less invasive method of surgery as compared to open surgery. However, indirect vision, limited hand movement and lack of haptic sensation, combined with the tiring posture of holding long tools makes it a very difficult task for the surgeon to perform (Tendick, 93; Faraz, June, 95). Consequently, the surgeon has a fraction of the dexterity and sensing of that of open surgery. This is specially the case in laparoscopic surgery which is a specific branch of endoscopic surgery, and is performed on the abdomen. The dexterity problem associated with laparoscopic surgery arises from the fact that the present rigid stem extenders can approach the surgical site with some fix orientation (determined by the connecting line between the position of surgical site and the port of entry). Lack of 2 DOF at the stem, to orient the tool’s tip to the desired orientation near the surgical site, prevents the surgeon from having the required dexterity and agility. By adding revolute/spherical joints on the stem, the required internal capability in orienting the tool can be achieved, and hence provide more dexterity for the surgeon. Although, there has been some publication in the literature about different design possibilities (e.g., Rinninsland, 93; Melzer, 93; Neisius, 94), as well as U.S. patents (Matsumaru, 92; Heimberger, 94), they are all dealing with special designs with specific design focus. There is a lack of general study of flexible endoscopic extenders with wider design objectives. For example, such objectives can be: (a) general type synthesis of the joint design, (b) formulation of workspace requirements of laparoscopic extenders, and (c) comparative study of different designs in search of the optimal design(s). The objective of this report is to have a systematic synthesis of the joints, as well as formulate the dexterous workspace for laparoscopic extenders with flexible stem, in order to find the optimum design.