Darwin Lau

Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach

In this paper, a technique to generate the wrench-closure workspace for general case completely restrained cable driven parallel mechanisms is proposed. Existing methods can be classified as either numerically or analytically based approaches. Numerical techniques exhaustively sample the task space, which can be inaccurate due to discretisation and is computationally expensive. In comparison, analytical formulations have higher accuracy, but often provides only qualitative workspace information. The proposed hybrid approach combines the high accuracy of the analytical approach and the algorithmic versatility of the numerical approach. Additionally, this is achieved with significantly lower computational costs compared to numerical methods. It is shown that the wrench-closure workspace can be reduced to a set of univariate polynomial inequalities with respect to a single variable of the end-effector motion. In this form, the workspace can then be efficiently determined and quantitatively evaluated. The proposed technique is described for a 3-DOF and a 6-DOF cable driven parallel manipulator. A detailed example in workspace determination using the proposed approach and comparison against the conventional numerical approach are presented.

Generalized Modeling of Multilink Cable-Driven Manipulators With Arbitrary Routing Using the Cable-Routing Matrix

Multilink cable-driven manipulators offer the compactness of serial mechanisms while benefitting from the advantages of cable-actuated systems. One major challenge in modeling multilink cable-driven manipulators is that the number of combinations in the possible cable-routing increases exponentially with the number of rigid bodies. In this paper, a generalized model for multilink cable-driven serial manipulators with an arbitrary number of links that allow for arbitrary cable routing is presented. Introducing the cable-routing matrix (CRM), it is shown that all possible cable routing can be encapsulated into a single representation. The kinematics and dynamics for the generalized model are derived with respect to the CRM. The advantages of the proposed representation include the simplicity and convenience in modeling and analysis, where all cable routing is inherently considered in a single model. To illustrate this, the inverse dynamics analysis is performed for two example systems: a 2-link 4-DoF manipulator that is actuated by 6 cables and an 8-link 24-DoF mechanism actuated by 76 cables. The results show the validity and scalability of the generalized formulation, allowing for complex systems with arbitrary cable routing to be modeled and analyzed.

Specular reflection of cold caesium atoms from a magnetostatic mirror

We have observed specular reflection and multiple bounces of a beam of laser-cooled caesium atoms from a magnetostatic mirror consisting of an array of rare-earth permanent magnets. Using a time-of-flight absorption technique, the reflection coefficient of the mirror for caesium atoms pumped toward the m=+4 state is determined to be . For a beam of unpolarized atoms the reflectivity is found to be unexpectedly high, , which is attributed to contributions from atoms in m = 0, -1, -2 states which are reflected at high magnetic fields close to the surface of the mirror as a result of the quadratic Zeeman effect.

Musculoskeletal Static Workspace Analysis of the Human Shoulder as a Cable-Driven Robot

The workspace analysis of cable-driven parallel manipulators has been widely studied, where the cables have been considered as ideal force generators. Due to the differences in actuation dynamics, workspace analysis has not been previously conducted for musculoskeletal systems. In this paper, static workspace analysis is performed on the human shoulder with a Hill-type physiological muscle model. The key characteristic of physiological muscles is that its ability to produce force is dependent on its length. Such type of workspace analysis on musculoskeletal systems as cable-driven manipulators is proposed for the first time. The generated shoulder workspace is validated by comparing the range of motion to that from benchmarks of human data. The significance of considering physiological muscles is demonstrated by comparing the musculoskeletal workspace with that of systems with ideal force generators. The novel formulation provides a new computational approach to perform workspace analysis for a wider range of engineered and biological systems.

Inverse Dynamics of Multilink Cable-Driven Manipulators With the Consideration of Joint Interaction Forces and Moments

Joint interaction forces and moments play a significant role within multilink cable-driven manipulators (MCDMs). In this paper, the consideration of joint interaction forces and moments in the objective function and constraints specific to the inverse dynamics of MCDMs are considered for the first time. By formulating the relationship between the joint interactions and cable forces, it is shown that the minimization of the joint interactions results in a convex quadratic program. Furthermore, the inclusion of constraints to maintain the stability of unilateral spherical joints results in a quadratically constrained quadratic program. Simulation results of the proposed formulations on two-link eight-cable and eight-link 76-cable manipulators are compared with the traditional two-norm cable force minimization. Results show that the formulations are able to take advantage of the actuation redundancy in considering the joint interactions within the inverse dynamics of MCDMs.

Manipulating beams of ultra-cold atoms with a static magnetic field

We report preliminary results on the deflection of a beam of ultra-cold atoms by a static magnetic field. Caesium atoms trapped in a magneto-optical trap (MOT) are cooled using optical molasses, and then fall freely under gravity to form a beam of ultra-cold atoms. The atoms pass through a static inhomogeneous magnetic field produced by a single current-carrying wire, and are deflected by a force ▽(µB) dependent on the magnetic substate of the atom. The population of atoms in various magnetic substates can be altered by using resonant laser radiation to optically pump the atoms.

Cable Function Analysis for the Musculoskeletal Static Workspace of a Human Shoulder

The study of cable function allows the contribution of particular cables towards the generation of motion to be determined for cable-driven parallel manipulators (CDPMs). This study is fundamental in the understanding of the arrangement of cables for CDPMs and can be used within the design of optimal cable arrangements. In this paper, the analysis of cable function for the musculoskeletal static workspace of a human shoulder is performed. Considering the muscles within the shoulder as state dependent force generators, the set of muscles required in sustaining the gravity force is determined for each workspace pose. As a result, the set of poses that each muscle is responsible for (muscle function) can be computationally determined. By comparing the results to the muscle function from biomechanics studies, it is shown that the results from the proposed cable function analysis are consistent with that reported in the literature of human studies.

On the Task Specific Evaluation and Optimisation of Cable-Driven Manipulators

Cable-driven manipulators are traditionally designed for general performance objectives, such as maximisation of workspace. To take advantage of the reconfigurability of cable-driven mechanisms, the optimisation of cable-configurations for specific tasks is presented. Specifically, two types of task specific objectives are explored, the minimisation of cable forces over a desired trajectory and the maximisation of workspace about a desired pose. The formulation and incorporation to the optimisation problem for both task specific objectives are presented. Illustrated using a 3-DoF manipulator example, the results clearly demonstrated the advantages of optimising cable configurations for specific tasks. The potential ease of relocation in cable attachments makes task dependent reconfiguration feasible.

Magnetostatic state-selective deflection of a beam of laser-cooled atoms

Abstract We have demonstrated the transverse state-selective deflection of a beam of free-falling laser-cooled caesium 6 2 S 1 2 , F = 4 atoms by the inhomogeneous static magnetic field of a current-carrying wire. With currents of up to 45 A the positions of atoms in individual magnetic substates are clearly resolved and deflection angles as large as 25° are observed. By optically pumping the atoms toward the m F = 4 substate in the ground state, most of the atoms are deflected through the same angle. The current-carrying wire can be considered as a simple magnetostatic atomic-optical element.

Conditions on the Cable-Routing Matrix for Wrench Closure of Multilink Cable-Driven Manipulators

Wrench-closure is an important property of cable-driven parallel manipulators (CDPMs), representing the ability to generate wrench in any direction by positive cable forces. For single link CDPMs, it is well known that m ≥ n + 1 cables are necessary for an n degrees-of-freedom CDPM to achieve wrench-closure. However, for multilink cable-driven manipulators (MCDMs), this condition is too relaxed and the cable routing should also be considered. In this paper, necessary conditions to achieve wrench-closure for MCDMs are mathematically derived based on the cable routing arrangements. Since the approach is independent on the exact attachment locations, the proposed necessary conditions can be efficiently validated during the design and synthesis of MCDMs. Analysis is performed on a range of different MCDM structures to identify cable arrangements that do not satisfy wrench-closure for an MCDM.