Reciprocal Screw Theory Research Articles

Disain CAD Mekanisme Paralel Tiga Derajat Translasi Murni Dengan Rantai Kinematik Kombinasi Sambungan Revolut dan Prismatik


 
 
 
 In this study it was discussed kinematic design of a 3-RRRPP translational parallel mechanism. The design was carried out by using simulation performed using CAD software. Motion platform was analyzed based on screw and reciprocal screw theory. The evaluation mechanism performance was determined by introducing the stages of research in the form to determine mechanism parts such as base, links, and platform. The work was continued with the assembly process of each part. Furthermore, kinematic response represented by displacement of platform positions was figured out by a CAD simulation. Based on the results of the simulation, it was successfully designed the mechanism performing the translational motion of the Platform.
 
 
 
 
 

Kinetostatics of Deployable Concrete Formworks

Abstract To reform the traditional concrete formwork, an overconstrained deployable frame is designed. It is composed of closed-loop deployable units formed by scissor-form elements and orthogonal telescoping rods. Using the reciprocal screw theory, the mobility of the deployable frame is studied, and it has one degree of freedom (DoF). To analyze the kinematic performance of the frame in the deployment and folding processes and the static characteristics under external loads at different deployed states, a general approach to analyzing the kinematics and statics by modeling in screw form is proposed. The velocities of joints could be solved in screw coordinates, the position and acceleration of joints could be obtained via a first-order numerical integration and a first-order numerical differential interpolation, respectively. Then, the position information for each joint can be forwarded onto the static equilibrium equations. Through the static analysis at each deployed state, the inner forces in each rod and the active control forces are derived. Kinematics and statics are associated by using velocities as the global variable, which allows a unified analysis of mechanisms. This method is computationally highly efficient and also fits for kinematic and static analysis of different kinds of multi-rigid-body mechanisms.

Type synthesis of plane-symmetric deployable grasping parallel mechanisms using constraint force parallelogram law

Type synthesis methods of parallel mechanisms or metamorphic mechanisms have drawn rising interest for mechanism designers. However, existing synthesis approaches cannot synthesize both parallel mechanisms and metamorphic mechanisms. This paper develops a synthesis method of metamorphic mechanisms, which enables it to construct a family of 2-degree-of-freedom (DOF) deployable grasping parallel mechanisms. Namely, the originality of this paper is that it explores a common synthesis method for both parallel mechanisms and metamorphic mechanisms. First, a new type of grasping sub-mechanisms is designed. Then, a kinematic sub-chain is constructed after assembly of a base, a platform, and the grasping sub-mechanism, whose constraint-screw system is obtained using reciprocal screw theory. This constraint-screw system is further applied to derive the desired constraints of auxiliary sub-mechanisms using the constraint force parallelogram law. Subsequently, auxiliary sub-mechanisms are type synthesized based on such desired constraints. Finally, a class of parallel mechanisms is constructed by assembling the auxiliary and the kinematic sub-chain. Thus, this paper and related work generate fresh insight into synthesizing both single-DOF metamorphic mechanisms and 2-DOF parallel mechanisms.

Feasibility, planning and control of ground-wall transition for a suctorial hexapod robot

One of the key factors that affect the efficiency and scope of work of wall-climbing robots is how the climbing robot can achieve autonomous transition between adjacent vertical planes. This paper studies the problem of ground-wall transition of a self-developed suctorial wall-climbing hexapod robot (WelCH). In view of the feasibility of the robot performing transition, this paper makes a detailed analysis of the number and property of degrees of freedom (DOFs) of the body and the foot based on reciprocal screw theory, and the results show that the robot can achieve transitional motion only when its home configuration is axisymmetric rather than radially symmetric. For realizing the robot’s ground-wall transition, based on a Sinusoid-Sigmoid-Shaped (SS-Shaped) interpolation function, the motion strategies of foot transferring and body pitching are firstly designed in detail. This interpolation method can effectively avoid the wear of the suction cups by relying on fewer essential path points. Then, the saturation-truncated method and mean filtering method are used to deal with joint constraints and abrupt changes in angular velocities. Finally, a kinematic-based adaptive sliding mode control (ASMC) is adapted to track the planned smooth trajectory, which can effectively resist bounded external disturbances. The successful transitions from the horizontal ground to the vertical wall for the robot WelCH in simulation and filed experiment demonstrate the effectiveness of the proposed strategy.

Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis

Stiffness is one of the critical performance indexes for robotic manipulators. In this study, a method for establishing the stiffness models of n(3RRlS) reconfigurable series-parallel manipulators (RSPMs) is proposed by combining the virtual joint method and matrix structural analysis. First, the constraint wrench system of the 3RRlS reconfigurable parallel manipulator (RPM) is obtained based on the reciprocal screw theory. Second, the stiffness matrices of the limbs along the axes of the constraint wrenches are analyzed using matrix structural analysis, and the overall stiffness matrix of the limbs is then assembled. Third, the stiffness matrices of the 3RRlS RPM and the n(3RRlS) RSPM are successively derived using the principle of virtual work. Finally, the theoretical and the finite-element-analysis deformations of the 3RRlS RPM and 3(3RRlS) RSPM are solved, and their average relative error is within 3.78%. It can be concluded that increasing actuation constraints can effectively improve the stiffness of manipulators in the directions of six degrees of freedom (DOFs) while increasing structural constraints can effectively improve the stiffness of manipulators in the directions of constrained DOFs.

Kinematics analysis of a novel 2R1T 3-PUU parallel mechanism with multiple rotation centers

In this paper, we present a novel three-degree-of-freedom (3-DOF) 3-PUU parallel mechanism (PM) with multiple rotation centers. Having two rotational DOFs and one translational DOF, the 3-PUU parallel robot consists of a fixed platform, a movable platform, and three identical PUU branches. Each PUU branch is composed of one prismatic(P) joint and two universal(U) joints. The mobility of initial configuration of the 3-PUU PM is analyzed using the reciprocal screw theory. Analysis of the 3-PUU PM's mobility of general configuration is performed based on its geometrical characteristics. The movable platform of the 3-PUU PM is demonstrated to be capable of rotating around multiple points. The singularities of 3-PUU PM are discussed. Using the inverse kinematics method, the workspace is obtained. Numerical examples are provided to illustrate the motion characteristics of the 3-PUU PM as a mechanism with multiple rotation centers.

Type synthesis of overconstrained 2R1T parallel mechanisms with the fewest kinematic joints based on the ultimate constraint wrenches

“Two rotational degrees of freedom” and “one translational degree of freedom” (2R1T) parallel mechanisms (PMs) have been successfully applied to develop five-axis hybrid robots for machining purposes. However, the number of passive joints contained in current 2R1T PMs has not still reached the minimum, which may impede these robots from having high stiffness. This study has put forward the concept of ultimate constraint wrenches acting on the PM's moving platform, and this concept was used to reduce the number of kinematic joints to a minimum. Based on the reciprocal screw theory, an ultimate constraint wrench system of the 2R1T PMs was found, and then a series of novel overconstrained 2R1T PMs with the fewest kinematic joints, containing three or four branches, were constructed. Furthermore, based on a developed overconstrained four-branch 2R1T PM RPU-2UPR-RPR, a type of five-axis hybrid robot with the fewest kinematic joints was constructed, which demonstrated good application prospects.

Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

The most general continuous rigid motion can be described by a curve in SE(3) of whose tangent vector the left or right invariant representation is a curve in se(3). The integral operation between them has not been achieved because there is no general solution for a system of the first-order linear differential equations with variable coefficients in mathematics. This paper develops a matrix equation (termed as the fundamental equation) based on the geometric properties of a pair of conjugate axodes equivalent to a curve in se(3) in algebras to achieve this integral operation. Moreover, the first-order and second-order derivations of the fundamental equation are derived. Furthermore, an algebraic method representing the body and spatial velocity twists as vector functions of dimensions and input parameters of mechanisms is founded on the theory of reciprocal screws. After that, this method and the fundamental equation are validated by the numerical examples of Bennett, spherical and planar four-bar linkages. Finally, this work presents a notion of generalized-involute which is a useful tool in the study of gear tooth profile and cam profile.

Modelling and analysis for a cylindrical net-shell deployable mechanism

Existing cylindrical deployable structures have poor controllability of deployment or weak bearing capacity. In order to satisfy the application needs of cylindrical deployable structures in the space industry, a cylindrical net-shell deployable mechanism is established in this article. The proposed cylindrical net-shell deployable mechanism has a regular cuboid shape in the folded state and a truss structure in the deployed state, and it can fit cylindrical surface, parabolic cylindrical surface, sine cylindrical surface and so on. Furthermore, based on reciprocal screw theory and screw synthesis theory, the mobility of cylindrical net-shell deployable mechanism in the whole motion cycle is analysed by the proposed equivalent model method. Results show that the cylindrical net-shell deployable mechanism is a single-degree-of-freedom mechanism. Moreover, a prototype is manufactured, and its motion performance is tested. The experiment shows that the cylindrical net-shell deployable mechanism has a smooth motion performance, and the mobility analysis method for complex coupled mechanism in this study is valid. This study has a certain significance in expanding the application field of cylindrical shell structure.

A Simple Method to Solve the Instantaneous Kinematics of the 5-RUR Parallel Manipulator

SummaryIn this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

Kinematics of the 3(RPSP)-S Fully Spherical Parallel Manipulator by Means of Screw Theory

In this work, the kinematics of a spherical parallel manipulator composed of three peripheral limbs equipped with linear actuators and a passive center shaft is approached by means of the theory of screws. The displacement analysis is carried out solving closure equations, which are obtained upon simple linear combinations of the components of two unit vectors describing the orientation of the moving platform. After, the input-output equations of velocity and acceleration of the spherical parallel manipulator are systematically obtained by resorting to reciprocal-screw theory. This strategy avoids the computation of the passive joint velocity and acceleration rates of the robot manipulator. Numerical examples illustrate the efficiency of the proposed method.

Type Synthesis of the Deployable Mechanisms for the Truss Antenna Using the Method of Adding Constraint Chains

In the deployable mechanism for a conventional truss antenna, the nodes cannot be adjusted to be uniform in attitude. To solve this problem, a method of adding constraint chains is proposed based on the reciprocal screw theory. By performing type synthesis of the deployable mechanisms for the truss antenna, a novel deployable mechanism is developed that not only enables complete folding and unfolding but also allows the attitude of the nodes to be made uniform. First, according to the unit division of the antenna reflection surface and the characteristic motions of the nodes, constraint chains that can be added between two adjacent nodes are synthesized based on the reciprocal screw theory. Second, to improve the overall rigidity of the mechanism, a series of basic developable unit mechanisms is obtained by adding virtual constraint chains, again based on the reciprocal screw theory. Next, a method of dividing the minimum combination unit of the curved-surface antenna mechanism is proposed. The design of the minimum combination unit mechanism is optimized, such that the attitude of all nodes in the final folded state can be made consistent. Finally, the feasibility of the optimized minimum combination unit mechanism is verified by simulation analysis. The proposed method for type synthesis provides a new approach to the design of deployable mechanisms for truss antennas, and novel deployable mechanisms for the curved-surface truss antenna with better performance are obtained.

Kinematics of the 4-RUU parallel manipulator generator of the Schönflies motion by means of screw theory

This work deals with the inverse–forward kinematic analysis of a symmetric parallel manipulator equipped with a rotary actuator generator of three independent translations and one rotation motion. The closure equations of the displacement analysis are easily formulated based on the unknown coordinates of two points embedded in the moving platform. The input–output equations of velocity and acceleration of the robot are systematically obtained through the reciprocal-screw theory. The pseudo-kinematic pairs that connect the limbs to the fixed platform and a passive kinematic chain connected to the robot manipulator eliminate the handling of rank-deficient Jacobian matrices, which is an undisputable advantage from the computational point of view. Furthermore, this strategy allows the use of the Lie algebra se(3) without the inherent restrictions associated with the limited mobility of the robot.

A new approach for the identification of reciprocal screw systems and its application to the kinematics analysis of limited-DOF parallel manipulators

The theory of reciprocal screws plays an important role in the kinematics and statics analysis of robot manipulators. Thus, efficient algorithms are usually required to identify the reciprocal screw system in closed-form. Inspired by the spatial stiffness/compliance, this paper presents a new approach for the identification of reciprocal screw system for any given one. The concept of symmetric screw matrix is introduced to uniformly represent the screw systems with 6 × 6 symmetric positive semidefinite matrices. By means of the change of coordinates and the recombination of base elements, any screw system can be decomposed into the direct sum of a general subsystem and a special one, which comprise only finite- and infinite-pitch elements belonging to the original system, respectively. Hence, for an arbitrary screw system, the corresponding reciprocal system can be achieved as the direct sum of those reciprocal to its subsystems. In the proposed framework, the decomposed subsystems can be uniquely identified by a diagonal and a symmetric 3 × 3 matrices, respectively, with respect to a particular choice of coordinate frame. Based on the theory of orthogonal complement spaces, the reciprocal subsystems can then be obtained in a straightforward manner with intuitive geometric interpretation. To verify the effectiveness of the proposed method in the kinematics analysis of limited degree-of-freedom (DOF) parallel manipulators, several typical candidates are investigated as examples. In all these examples, the screw systems can be identified in closed-form and the instantaneous kinematics can be characterized according to the properties of the obtained subsystems.

Análisis Cinemático del Manipulador Paralelo 4-PRUR Mediante la Teoría de Tornillos

In this work the kinematics of a parallel manipulator performing Schönflies motion is investigated by means of the theory of screws. As an intermediate step, the displacement analysis is reported in semi-closed form solution based on the coordinates of two points embedded in the moving platform. This strategy allows to employ only one reference frame avoiding the computation of the rotation matrix. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. To this aim, the robot is treated as a six-degrees-of-freedom parallel manipulator incorporating pseudo kinematic pairs connecting the limbs to the fixed platform and one virtual kinematic chain in order to apply without restrictions the Lie algebra se(3) of the Euclidean group SE(3). The singularity analysis is investigated based on the input-output equation of velocity. Numerical examples are included in order to show the application of the method.

Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

Type Synthesis of fully-Decoupled 2T2R Parallel Mechanisms Based on Driven-Chain Principle

Based on the screw theory and the driven-chain principle, a methodology of structural synthesis for fully-decoupled two-translational (2T) and two-rotational (2R) parallel mechanism is proposed by analyzing the characteristics of the input-output relations for fully-decoupled parallel mechanisms. Firstly, according to the desired kinematic characteristics of fully-decoupled parallel mechanisms, a method is proposed by virtue of screw theory to synthesize the desired forms for both the direct and the inverse Jacobian matrices. Secondly, according to the feature of the direct and the inverse Jacobian matrices, the effective screws, the actuated screws and the mobile un-actuated screws of each leg are established based on the reciprocal screw theory and all possible topology structures fulfilling the requirements are obtained. Finally, the desired fully-decoupled parallel mechanisms can be synthesized by using the structural synthesis rule and structural synthesis of fully-decoupled 2T2R parallel mechanisms can be obtained exploiting the abovementioned methodology. In particular, the direct Jacobian matrix of each synthesized fully-decoupled 2T2R parallel mechanism is a non-zero diagonal matrix throughout the entire workspace. Motors are mounted on each leg and each one of them actuates one degree-of-freedom (DoF) of the fully-decoupled parallel mechanism through a one-to-one velocity relation.

Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

A novel 3-PUU parallel mechanism and its kinematic issues

The modules of parallel tool heads with 2R1T degrees of freedom (DOFs), i.e., two rotational DOFs and one translational DOF, have become so important in the field of machine tools that corresponding research has attracted extensive attention from both academia and industry. A 3-PUU parallel mechanism with 2R1T DOFs is first proposed in this paper, and a detailed discussion about its architecture and geometry constraints are presented. Furthermore, the mobility analysis of the proposed 3-PUU mechanism is carried out by resorting to the reciprocal screw theory. In addition, on the basis of its special geometry constraint conditions, the parasitic motion of 3-PUU mechanism is derived and explicitly expressed. Then the inverse kinematics problem (IKP), the Jacobian matrix calculation, and the forward kinematics problem (FKP) are investigated. At last, the motion/force transmissibility characteristics, the singularity properties, and the reachable workspace are discussed, respectively. The above analyses illustrate that the 3-PUU parallel mechanism owns good motion/force transmissibility and orientation capability, which validate the feasibility of applying this mechanism as a tool head module.

Kinematics of a Class of Three-Legged Parallel Manipulators by Means of Screw Theory

This work is devoted to the velocity and acceleration analyses of a class of three-legged parallel manipulators. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. With the purpose to exemplify the application of the method, a case study is included. The example consists of solving the kinematics of a 3-CRS (Cylindrical + Revolute + Spherical) parallel manipulator. Furthermore, the numerical results obtained via screw theory are verified with the aid of commercially available software.