Finite Screw Research Articles

A New Method for Displacement Modelling of Serial Robots Using Finite Screw

Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. Both of them depend on the displacement models. Compared with the previous work, finite screw is proven to be the simplest and nonredundant mathematical tool for displacement description. Thus, it is used for displacement modelling of serial robots in this paper. Firstly, a finite-screw-based method for formulating displacement model is proposed, which is applicable for any serial robot. Secondly, the procedures for forward and inverse kinematics by solving the formulated displacement equation are discussed. Then, two typical serial robots with three translations and two rotations are taken as examples to illustrate the proposed method. Finally, through Matlab simulation, the obtained analytical expressions of kinematics are verified. The main contribution of the proposed method is that finite-screw-based displacement model is highly related with instantaneous-screw-based kinematic and dynamic models, providing an integrated modelling and analysis methodology for robotic mechanisms.

Application of finite screw method for multi-mode mechanism classification and determination

To enrich the theoretical system of multi-mode mechanisms, a classification method and a determination method are proposed in this paper. From the perspective of configuration transformation, the multi-mode mechanisms are divided into two types: one based on lockable joints and the other based on the principle of bifurcated motion. Furthermore, the mechanisms based on the principle of bifurcated motion are categorized into two types: one based on the variable mobility branch and the other based on constraint singularity generated by branches. The principles of classification are expounded and the determination method is developed. The proposed classification and the determination methods of the multi-mode mechanism provide new insights for their analysis.

Structure Synthesis of 3-DOF Translational Parallel Mechanisms With Configurable Platform of Translation

Abstract The parallel mechanisms (PMs) with configurable platforms have the advantages of flexibility, high speed, and extra operability over PMs with common platforms. This paper proposes a systematic approach for synthesizing three-degrees-of-freedom (3-DOF) translational parallel mechanisms with configurable platforms of one translation DOF (TPMs-T) based on the finite screw. The motion relationship between the configurable platform and limbs is discussed to achieve the motion requirement of the TPMs-T limbs. The equivalence principle of kinematic joints is further pinpointed, and a series of lower mobility limbs have been developed. At last, the geometric relationship of assembly conditions is derived which can contribute to quickly solving the intersection of limb motions, a series of TPMs-T are constructed to verify the assembly conditions, and the fully controlled condition is discussed.

Configuration design and kinematics analysis of foldable composite space capture mechanism

To meet the requirements of high flexibility, high stiffness, and large working range of space debris cleaning technology, a foldable composite space capture mechanism is proposed based on the finite screw theory in this paper. The degree of freedom of the mechanism is analyzed by using the screw theory and its degree of freedom is obtained. The closed-loop vector method and DH method are used to analyze the kinematics of the mechanism, and the position solution of the mechanism is derived. The analytical expressions of velocity and acceleration solutions are obtained by differential calculation. According to the analysis of numerical example, the kinematic model of the mechanism is built in the simulation environment, and the simulation experiment is carried out for the motion trajectory of the mechanism. The correctness of theoretical analysis solution and method is proved by contrasting and analyzing motion trajectory, and it is verified that the space capture mechanism uses the foldable property to form large workspace to complete the capture of the target.

Space truss construction modeling based on on-orbit assembly motion feature

More space truss construction has been planned to develop and utilize space resources. These trusses are designed in the way of large-scale, complex, modular, and on-orbit assembly. To meet the upcoming challenge of large-scale space infrastructure construction, it is necessary to study space truss automation design and robotic construction. This paper proposes an ordinal finite screw adjacency matrix model (OFSAMM), focusing on the relationship between assembly motions, to express and compute a space truss structure. In this model, a space truss is abstracted as a set of ordered assembly motions, each of which is recorded as a finite screw as the basic element of the truss and its assembly. The operation of truss transformation is also derived under this model. Therefore, the truss configuration, the assembly sequence, the truss sub-assembly, the truss components, and the on-orbit assembly task can be expressed and calculated in a unified model, which is calculated and stores the truss topology and assembly with the minimum storage cost. At the end of this paper, we introduce how to synthesize and optimize space truss design through two cases. The study will help to improve design efficiency. Furthermore, it provides a theoretical basis for the automatic construction of space truss structures, especially in the next stage.

Task-Oriented Topology System Synthesis of Reconfigurable Legged Mobile Lander Integrating Active and Passive Metamorphoses

To explore hostile extraterrestrial landforms and construct an engineering prototype, this paper presents the task-oriented topology system synthesis of reconfigurable legged mobile lander (ReLML) with three operation modes from adjusting, landing, to roving. Compared with our preceding works, the adjusting mode with three rotations (3R) provides a totally novel exploration approach to geometrically matching and securely arriving at complex terrains dangerous to visit currently; the landing mode is redefined by two rotations one translation (2R1T), identical with the tried-and-tested Apollo and Chang’E landers to enhance survivability via reasonable touchdown buffering motion; roving mode also utilizes 2R1T motion for good motion and force properties. The reconfigurable mechanism theory is first brought into synthesizing legged mobile lander integrating active and passive metamorphoses, composed of two types of metamorphic joints and metamorphic execution and transmission mechanisms. To reveal metamorphic principles with multiple finite motions, the finite screw theory is developed to present the procedure from unified mathematical representation, modes and source phase derivations, metamorphic joint and limb design, to final structure assembly. To identify the prototype topology, the 3D optimal selection matrix method is proposed considering three operation modes, five evaluation criteria, and two topological subsystems. Finally, simulation verifies the whole task implementation process to ensure the reasonability of design.

Topology and Dimension Synchronous Optimization of 1T2R Parallel Robots

Parallel robots have attracted much attention from both academia and engineering in last two decades. For development of novel parallel robots, topology and dimensions are brought into sharper focus, which are associated closely and have coupled influence on both motion pattern and performance together. However, currently topology design and dimension design are always performed individually with independent aims, leading to local optimal solutions and difficulties in further modification. Actually, the intrinsic relationship between topology and performance is concerned far from abundant. In this article, a method for topology and dimension synchronous optimization is investigated by employing finite screw theory. Within this approach, two algorithms are formulated to parameterize and deliver topology characters in the same format with dimensions. Topology design and dimension design are converted into a synchronous optimization model with mixed variables and multi-objectives, resulting in global optimal solutions of both optimal topology and dimensions. Topology and dimension synchronous optimization of a kind of 1T2R parallel robots is presented and discussed by comparing with state-of-the-art methods.

Multi-Objective Optimization of 1T2R Parallel Mechanisms Without Fixed Orientation Center and Axis Under the Influence of Parameter Perturbation

To track moving targets and signals in space, multiple characteristics as large orientational workspace and excellent kinematic performance are required for the satellite antenna driving mechanism. Due to variable orientational center and axes, the 3-RSR mechanism is capable of 1T2R with continuous workspace and becomes a promising solution for the satellite antenna driving mechanism. Influenced by the topological structure characteristics as none fixed orientation center and axes, the performances of 3-RSR mechanism are significantly impacted by the parameter perturbation. According to the differential mapping between finite screw and instantaneous screw, the structure, kinematics, performance, and optimization are unified under the FIS theory. To be applied for the satellite antenna driving mechanism, this paper carries out the multi-objective optimization of 3-RSR mechanism under the influence of parameter perturbation based on the FIS theory. Firstly, the orientational workspace is obtained by finite screw and the instantaneous motion description of the mechanism is derived through calculation principle of FIS theory. Secondly, the orientational workspace and kinematics indices of the mechanism are proposed towards the actual requirements of the satellite antenna driving, and the relationship with the parameters is established. The discrete operation becomes extremely complex owing to parameter perturbation, and the RSMs (response surface model) of indices without considering and considering parameter perturbation are modeled. The multi-objectives optimization of 3-RSR mechanism influenced by parameter perturbation is carried out and its Pareto frontier is obtained. Finally, a point preferred strategy is proposed and the optimum value of the parameter from Pareto frontier is selected.

Type synthesis and performance analysis of manipulators with shape adaptability

Manipulators have attracted wide attention in recent years because they are simple and easy to control when grasping objects in space. However, there are not many theoretical researches on manipulator at present. Therefore, based on the principle of simple operation and low cost, a manipulator with high versatility, high flexibility, diverse movement modes, and shape adaptability has laid a solid theoretical foundation and practical significance for the innovative development of robot. In this paper, a 4-RRS& planar four-bar mechanism with bifurcation motion is proposed based on the finite screw theory. The degrees of freedom of the mechanism are analyzed by using the screw theory. Then the closed-loop vector method and instantaneous screw method are used to establish the analytical expression and the velocity Jacobian matrix between the motor actuation angle and the moving platform, respectively. Finally, on the basis of kinematic analysis, the SolidWorks and Matlab software are used to verify the kinematic simulation of the mechanism, so as to ensure the rationality of the mechanism motion and the correctness of the theoretical derivation.

Calibration for Precision Kinematic Control of an Articulated Serial Robot

Robot calibration to provide an accurate kinematic model is widely adopted in the advanced controller development of articulated serial robot performing complicated tasks. Conventional calibration methods mainly focus on the complete, continuous, and minimal error modeling. The generation and accumulation of errors have not been explicitly explained. In addition, the error identification and compensation sometimes are not practical for controller establishment. This article presents a robot calibration method using finite and instantaneous screw theory. From the differentiation of finite screw, the errors are defined by the deviations of instantaneous screws at initial pose. The error modeling is explicit. We also propose an advanced optimization algorithm based identification method and regard the geometry of redundant errors as constraints. The identified instantaneous screw errors are then converted to the joint actuation errors. Without modifying existing motion controller, errors are compensated by modified inputs. A UR3 robot is taken as an example to illustrate the calibration method. Simulation and experiment are implemented for verification. Comparing with the accuracy before calibration, the position and orientation accuracy of UR3 robot after calibration has improved by 94.75% and 89.29%. The results also show that modified inputs can be conveniently connected to controller development.

Compliant Mechanism as a Motion-Preserving Artificial Spinal Disc: A Novel Concept

Abstract Investigations of spinal disc replacement options have been conducted for several decades but, as yet, the suggested solutions have not been proven to correctly preserve the natural joint motion. This paper focuses on a new structure of an artificial intervertebral disc joint that closely supports a close-to-natural three-dimensional motion of two adjacent vertebrae. The disc design is based on a passive parallel mechanism, with different stiffnesses for each link. Optimization of the artificial disc dimensions and link stiffnesses enabled convergence of the finite screw axis (FSA) of the artificial disc joint with that of a natural disc. As a result, the natural motion of the spine vertebrae was maintained and the loads on the facet joints minimized. The mechanism design was optimized, built, tested, and proven to be a feasible artificial disc with natural motion preservation characteristics.

A Dual-Vector Method to Derive the Equivalent Screw of Two Successive Finite Screw Displacements for Line Segments

Abstract For finite rigid body motion, every two successive screw displacements can be represented by one equivalent screw displacement. However, such phenomenon should not be considered naturally to be valid for incompletely specified displacements (ISDs). There is neither a precise statement for such phenomenon nor an understanding of its range of validity within ISD, such as line segment displacements. As one of the main contributions in this paper, based on dual vector algebra and screw theory, an algorithm is provided to prove the existence of the subset within the scope of the line segment motion, which expresses the similar relation as shown in finite rigid body motion. A numerical example is presented for illustrative purpose.

Different Kinds of 3T2R Serial Kinematic Chains and Their Applications in Synthesis of Parallel Mechanisms

This paper proposes a new-kind three-translational and two-rotational (3T2R) motion with one fixed and one variable rotation directions. The serial kinematic chains (SKCs) that generate the proposed motions are synthesized. They are quite different from the SKCs generating 3T2R motion with two fixed rotation directions. Firstly, according to the relationships between the two rotations in a motion, the classification of 3T2R motions is discussed. By using finite screw as mathematical tool, the expressions of the two different kinds of 3T2R motions are formulated as algebraic sets. Secondly, serial motion generators of the 3T2R motions are investigated. The SKCs that generate the first-kind 3T2R motion are briefly reviewed; the twenty-eight types of SKCs that generate the second-kind 3T2R motion are synthesized by analytical derivations. Finally, the SKCs with the second-kind 3T2R motion are used to synthesize new parallel mechanisms. Two five-degree-of-freedom (five-DoF) systematical parallel mechanisms are taken as examples to show the applications of these SKCs. This paper provides theoretical foundations for the research on motions generated by complex SKCs and on motion patterns with variable rotation directions and centers.

Motion generators of quadric surfaces

This paper presents research work on synthesis of the mechanisms that generate translations on circular, cylindrical, and conical surfaces. As these three kinds of surfaces are all basic quadrics, the synthesized mechanisms are called motion generators of quadric surfaces. Firstly, the characteristics of these quadrics are analyzed, which result in an easy way to express them. Secondly, the motion sets of one-degree-of-freedom (one-DoF) joints are described by finite screws, leading to a simple and non-redundant manner for mechanisms’ motion description. Based upon this, the motion generators of circular, cylindrical, and conical surfaces are respectively synthesized, and all the serial kinematic chains that generate these quadrics are obtained. The results are verified through simulations in MATLAB software. Finally, as an application of the motion generators of quadrics, closed-loop linkages constituted by the generators of cylindrical and circular surfaces with specific geometric conditions are synthesized, which purely generate one-DOF translations along ellipse curves. Some new serial kinematic chains and closed-loop linkages are invented in this paper. These new mechanisms have simple mechanical structures, and they have potential applications in design of robots used in machining and manufacturing of complex surfaces and curves.

Dynamic modeling of a two-DoF rotational parallel robot with changeable rotational axes

Because of the outstanding capabilities to realize flexible orientations, the specific category of rotational parallel robots with changeable rotational axes have a wide application in design of bionic eyes, dexterous wrists, tracking and pointing devices. A two-DoF parallel robot in this category called Helix is studied in this paper. Employing a finite and instantaneous screw based method, dynamic modeling and analysis of Helix robot is presented, which provides a theoretical foundation for performance design and dynamic control. Firstly, concept description and inverse kinematics of Helix robot is given, which is the prerequisite for dynamic modeling and analysis. Secondly, twist and wrench based velocity, force and acceleration analysis of this robot is carried out, resulting in the Jacobian and Hessian matrices which are obtained through directly differentiating the finite screw based topological model. Then, using these matrices, its dynamic equation is formulated considering the gravity of each component. Finally, the obtained dynamic model of Helix robot is verified through comparing the simulation results in ADAMS and Matlab software. The finite and instantaneous screw based method used in this paper is a generic one which is suitable for dynamic modeling of different serial and parallel robots.

Type synthesis of 1T2R parallel mechanisms with parasitic motions

Finite motion analysis and type synthesis of parallel mechanisms with parasitic motions are great challenges in the fields of mechanisms and robotics. This paper proposes a finite screw based approach to handle this problem by taking one translational and two rotational (1T2R) parallel mechanisms with parasitic motions as examples. Firstly, 1T2R finite motion of the moving platform is categorized into four cases whose finite motions are described by finite screw analytically and then the reasons for producing parasitic motions are explored in this process. Based on this, available limbs are obtained algebraically by deriving formulas formed by triangle screw product. Finally, the assembly conditions among limbs, fixed base and moving platform are acquired in an analytical manner, leading to synthesize 1T2R parallel mechanisms with parasitic motions systematically. This paper solves a long-term problem that describes and analyzes finite motions of parallel mechanisms with parasitic motions and synthesizes their topology structures.

Fault-tolerant feature-based estimation of space debris rotational motion during active removal missions

One of the key functionalities required by an Active Debris Removal mission is the assessment of the target kinematics and inertial properties. Passive sensors, such as stereo cameras, are often included in the onboard instrumentation of a chaser spacecraft for capturing sequential photographs and for tracking features of the target surface. A plenty of methods, based on Kalman filtering, are available for the estimation of the target's state from feature positions; however, to guarantee the filter convergence, they typically require continuity of measurements and the capability of tracking a fixed set of pre-defined features of the object. These requirements clash with the actual tracking conditions: failures in feature detection often occur and the assumption of having some a-priori knowledge about the shape of the target could be restrictive in certain cases. The aim of the presented work is to propose a fault-tolerant alternative method for estimating the angular velocity and the relative magnitudes of the principal moments of inertia of the target. Raw data regarding the positions of the tracked features are processed to evaluate corrupted values of a 3-dimentional parameter which entirely describes the finite screw motion of the debris and which primarily is invariant on the particular set of considered features of the object. Missing values of the parameter are completely restored exploiting the typical periodicity of the rotational motion of an uncontrolled satellite: compressed sensing techniques, typically adopted for recovering images or for prognostic applications, are herein used in a completely original fashion for retrieving a kinematic signal that appears sparse in the frequency domain. Due to its invariance about the features, no assumptions are needed about the target's shape and continuity of the tracking. The obtained signal is useful for the indirect evaluation of an attitude signal that feeds an unscented Kalman filter for the estimation of the global rotational state of the target. The results of the computer simulations showed a good robustness of the method and its potential applicability for general motion conditions of the target.

Type synthesis of parallel mechanisms having 3T1R motion with variable rotational axis

Parallel mechanisms (PMs) having three translational (T) and one rotational (R) movement capability draw continuous attention from academia and industry. The existing 3T1R PMs can only generate Schoenflies motion and bifurcation of Schoenflies motion. This paper proposes a new 3T1R motion that features one rotation about a varying axis plus three pure translations. Drawing mainly on finite screw theory, a hierarchical approach for type synthesis of limb structures of the PMs having 3T1R motion with variable rotational axis is presented by developing the basic limb bonds first and then their equivalent substitutions using the properties of screw triangle product. The assembly conditions for the PMs of this kind are discussed. Consequently, numerous novel PMs consisting of four identical limbs are synthesized using this technique.

A way of relating instantaneous and finite screws based on the screw triangle product

It has been a desire to unify the models for structural and parametric analyses and design in the field of robotic mechanisms. This requires a mathematical tool that enables analytical description, formulation and operation possible for both finite and instantaneous motions. This paper presents a method to investigate the algebraic structures of finite screws represented in a quasi-vector form and instantaneous screws represented in a vector form. By revisiting algebraic operations of screw compositions, this paper examines associativity and derivative properties of the screw triangle product of finite screws and produces a vigorous proof that a derivative of a screw triangle product can be expressed as a linear combination of instantaneous screws. It is proved that the entire set of finite screws forms an algebraic structure as Lie group under the screw triangle product and its time derivative at the initial pose forms the corresponding Lie algebra under the screw cross product, allowing the algebraic structures of finite screws in quasi-vector form and instantaneous screws in vector form to be revealed.

A finite screw approach to type synthesis of three-DOF translational parallel mechanisms

This paper for the first time presents a finite screw approach to type synthesis of three-degree-of-freedom (DOF) translational parallel mechanisms (TPMs). Firstly, the finite motions of a rigid body, a TPM and its limbs are described by finite screws. Secondly, given the standard form of a limb with the specified DOF, the analytical expressions of the finite screw attributed to the limb are derived using the properties of screw triangle product, resulting in a full set of the 3-, 4- and 5-DOF limbs that can readily be used for determining all the potential topological structures of TPMs. Finally, the assembly conditions for type synthesis of TPMs are proposed by taking into account the inclusive relationship between the finite motions of a TPM and those of its limbs. The merit of this approach lies in that the limb structures can be formulated in a justifiable manner that naturally ensures the full cycle finite motion pattern specified to the moving platform.