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The solution and simulation analysis of the singularity configurations within its workspace of the seven axis cooperative KUKA manipulator is presented. Firstly， the manipulator kinematics model is constructed and the DH parameter is obtained. Secondly， the Jacobian matrix is computed based on screw theory and the screw reciprocity method is used to find the singularity configurations. Finally， the dexterity of end reference point of robot is analyzed based on manipulability index and the minimum singular value index by means of the Robotics Toolbox. The analysis results reveals that there are four singular conditions of the seven axis cooperative KUKA robot within its workspace， and the simulation results verifies the correctness of the analysis， and it lays a foundation for subsequent manipulator singularity avoidance arithmetic research.

The paper proposes a solution to an inverse kinematics problem based on dual quaternions algebra. The method, relying on screw theory, requires less calculation effort compared with commonly used approaches. The obtained kinematic description is very concise, and the singularity problem is avoided. The dual quaternions formalism is applied to the problem decomposition and description. As an example, the kinematics problem of a multi-DOF serial manipulator is considered. Direct and inverse kinematics problems are solved using division into sub-problems. Each new sub-problem proposed is concerned with rotation about two subsequent axes by a given amount. The presented example verifies the correctness and feasibility of the proposed approach.

Aiming at the functional requirements of mobile mechanisms with multiple modes，a design scheme based on single-loop kinematic chains is proposed.Firstly，according to the single-loop freedom formula，the conditions satisfying the single-loop and can be active are determined，and the combination relationships among the order of the constrained screw system，the number of bars，the number of kinematic pairs and the degree of freedom of the single-loop kinematic chains are obtained.Secondly，based on the screw theory，the geometric conditions of the axis of kinematic pairs under different constrained screw orders are obtained by using the virtual work principle.Taking the R and P pairs as the design units，all the possible combinations of the single-loop kinematic chains under different degrees of freedom are enumerated，and then the constructed single-loop kinematic chains are used as the body or branch to construct a kind of mobile mechanisms with multiple modes.Finally，the steps of type synthesis of mobile mechanisms with multiple modes and some design cases are given，which verifies the feasibility and practicability of the proposed design theory and design method.

Abstract To assist an amputee in regaining his or her daily quality of life, based on analysis of the motion characteristics of the human hip, a 2-UPR/URR parallel mechanism with a passive limb was designed. The inverse kinematics of this mechanism was analyzed based on a closed-loop vector method. The constrained Jacobian matrix and kinematic Jacobian matrix of each limb were then analyzed, and a 6 × 6 fully Jacobian matrix was constructed. Based on this, kinematic performances were analyzed and summarized. Finally, the dynamic model of the mechanism was constructed based on the virtual work principle, and its theoretical solution was compared with the numerical results, which were obtained in a simulation environment. Results showed that the prosthetic mechanism had a larger rotating workspace and better mechanical performance, which accorded a range of motion and bearing capacity similar to that of the human hip in multiple gait modes. Moreover, the validity of the dynamic model and inverse kinematics were verified by comparing the theoretical and simulation results. Furthermore, with flexion and extension, the torque change in the hip prosthetic mechanism was similar to that of the human hip, which demonstrated the feasibility of the hip prosthetic mechanism and its good dynamic performance.

This paper proposes the systemic dynamic modeling and analysis of a 2PRU-UPR parallel robot with two rotations and one translation based on screw theory, where P, R and U denote prismatic, revolute and universal joints, respectively. Compared with existing parallel robots having two rotations and one translation, the two actuated prismatic joints of the 2PRU-UPR parallel robot are mounted on a fixed base to reduce the movable mass and improve the dynamic response. First, the inverse kinematics are presented. Next, adopting the screw-based method, the velocity and acceleration of joints and limbs of the 2PRU-UPR parallel robot are analyzed in detail. The actuated forces of the three actuators are then obtained according to the principle of virtual work. Additionally, a numerical simulation is conducted using ADAMS software to investigate the dynamic model of the 2PRU-UPR manipulator and to verify the correctness of the theoretical results. Finally, distributions of the dynamic manipulability ellipsoid index are used to evaluate the dynamic translational and rotational performances of the 2PRU-UPR parallel robot. A prototype based on the dynamic analysis has been fabricated. The dynamic modeling and evaluation provide a basis for the efficient and precise control of the 2PRU-UPR parallel robot in actual machining manipulations. The 2PRU-UPR parallel robot has great potential in machining workpieces with curved surfaces.

This paper proposes a geometric approach to the conditions for mode decoupling of a vibration system of an elastically supported single rigid body and presents the conditions that the system has only pure rotation modes of vibration. A small oscillation of a rigid body is indeed a repetitive screw motion and thus vibration modes are expressed by screws in general, which results in the difficulty involved in solving a vibration problem. The complexity of a vibration system can be alleviated for both analysis and synthesis if the system has only rotation modes. In order to acquire the decoupling techniques, this paper begins by investigating a stiffness matrix which can be separated into the sum of two rank 3 stiffness matrices, which are realizable by using co-reciprocal line vectors. From the co-reciprocity, the separable stiffness matrix can be regarded as a linear transformation between two 3-systems of screws containing only line vectors. Using the properties of the linear transformation and the screw systems, the conditions for mode decoupling, or the conditions for only pure rotation modes are derived and described by geometric relations between inertia and stiffness, and three cases of vibration systems with simple geometric nature are identified.

A reduced dynamic modeling approach is introduced to systematically establish explicit closed-form dynamic equations for the main motion system of a heavy-duty hydraulic manipulator with multi-closed-loop mechanisms. The harmonious combination of the reduced system dynamic method with Lagrangian formulation, the principle of virtual work and screw theory greatly reduces the tedious calculation and largely simplifies the derivation of explicit control-orientated closed-form dynamic equations for complex multi-closed-loop mechanisms. Only three coupled subsystems, two Jacobian matrices, and two Hessian matrices are involved, thereby greatly reducing the order and the complexity of the closed-form dynamic equations. In addition to calculating the two Jacobian matrices by screw theory, the two Hessian matrices are also calculated straightforwardly by screw theory, thereby avoiding the difficulty in obtaining Hessian matrices by differentiating the Jacobian matrices and simplifying the calculation of the two Hessian matrices. No parts of dynamic equations are neglected in the derivation of the dynamic model. Thus, the accurate dynamic motion equations for the main motion system are obtained concisely. The derived closed-form dynamic equations are explicit with respect to the system inputs, which facilitate dynamics analysis and controller design. The experiments on the main motion system of the heavy-duty hydraulic forging manipulator demonstrate the efficiency of the proposed approach.

Mobile parallel mechanisms (MPMs), which are parallel mechanisms with moveable bases, have previously been proposed to resolve the limited workspace of conventional parallel mechanisms. However, most previous studies on the subject focused on the kinematic analysis of some specific MPMs and did not discuss a type synthesis method for MPMs. With this in mind, we propose a screw theory-based type synthesis method to find out possible 6-degrees-of-freedom (DOF) MPM structures. In our proposed method, the 6-DOF mobility is divided into 3-DOF planar motion and 3-DOF spatial motion, both of which are realized by the transmitted planar motions of the driving units. Separately, the type synthesis of the entire MPM is divided into that of the driving unit and connecting chain. To realize 3-DOF spatial motion, two methods, applying singularity configuration and adding an additional chain, are proposed as ways to restrict undesired motions for the synthesis of the connecting chain. The driving unit is synthesized via the same type-synthesis method as the connecting chain by considering the driving unit as a planar mechanism. The method used to integrate the driving unit and the connecting chain was constructed based on whether the end pair of the connecting chain should be connected with the driving unit directly or driven by it through an actuating mechanism. As a result, 284 possible types of MPM structure are suggested and four examples of MPMs with six DOFs were synthesized to verify the feasibility of the proposed method.

The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obtaining the laws of control directly with screws and co-screws, which is considered modern robotics by diverse authors. In addition, geometric algebra (GA) is introduced as a simple and iterative tool to obtain screws and co-screws. On the other hand, such as the controllers, the Hamiltonian equations of motion (in the phase space) are developed using co-screws and screws, which is a novel approach to compute the dynamic equations for robots. Regarding the controllers, two laws of control are designed to ensure the error’s convergence to zero. The controllers are computed using the traditional feedback linearization and the sliding mode control theory. The first one is easy to program and the second theory provides robustness for matched disturbances. On the other hand, to prove the stability of the closed loop system, different Lyapunov functions are computed with co-screws and screws to guarantee its convergence to zero. Finally, diverse simulations are illustrated to show a comparison of the designed controllers with the most famous approaches.

The motion path of the developable mechanism can not only grasp whether the mechanism can move according to the expected law, but also provide theoretical support for motion control. In order to accurately study the kinematics of the square combined mechanism, the mobility of the square combined expandable mechanism is analyzed based on the screw theory and the graph theory. Then, the balance matrix of the square combined expandable mechanism is derived, and the displacement mode of the square combined expandable mechanism is obtained through singular value decomposition. Secondly, the path tracking method of the square combined expandable mechanism is established by the iteration of the displacement mode. Finally, by means of the example analysis, the position of the bifurcation point of the square combined expandable mechanism is determined; the variation law of the bifurcation point and its positive correlation with the singular value of the balance matrix is analyzed. It is found that adding additional constraints and planning a reasonable path can avoid bifurcation phenomenon. This research provides necessary reference data for configuration design and parameter optimization of the square combined expandable mechanism.

Dynamic locomotion plays a crucial role for legged robots to fulfill tasks in unstructured environments. This paper proposes whole-body kinematic and dynamic modeling method s based on screw theory for a quadruped robot using different gaits and mechanism topologies. Unlike simplified models such as centroid or inverse pendulum models, the methods proposed here can handle 10-dimensional mass and inertia for each part. The only simplification is that foot contact models are treated as spherical joints. Models of three different mechanism topologies are formulated: (1) Standing phase: a system consisting of one end-effector, the body, and four limbs, the legs; (2) Walking phase: a system consisting of one or two lifting legs (depending on the chosen gait), two or three supporting legs; (3) Floating phase: a system in which all legs detach from the ground. Control strategies based on our models are also introduced, which includes walk and trot gait plans. In our control system, two additional types of information are provided: (1) contacting forces are given by force sensors installed under feet; (2) body poses are determined by an inertial measurement unit (IMU). Combined with the sensor data and calibrated mass, inertia, and friction, the joint torque can be estimated accurately in simulation and experiment. Our prototype, the “XiLing” robot, is built to verify the methods proposed in this paper, and the results show that the models can be solved quickly and leads to steady locomotions.

In this paper, a two-way self-adaptive gripper that has adaptability to external disturbance loads during linear opening/closing pinch actions and adaptability to encompass a variety of shapes during grasping using a single actuator is proposed, unlike the previous self-adaptive robotic grippers capable of only shape adaptation. Therefore, both linear motion adaptability and shape adaptability during parallel grasping situations are enabled by the proposed design of the gripper. Adaptation to the linear pinch motion is provided through the use of a differential gear, the two outputs of which drive the two tips of the gripper. If facing uneven external loads, the differential gear adaptively alters the speeds of the two outputs, resulting in different closing speeds of the two gripper tips. Despite asymmetric closing, very stable grasping can be guaranteed for such a situation. The differential gear can even complete the grasping by intentionally or unintentionally fixing one of the gripper tips. The proposed design is also capable of shape adaptation in the encompassing grasping mode by adopting a parallel-linkage gripper mechanism, consisting of an exoskeleton and 6 internal joints with a spring element. The finger exoskeleton facilitates pinch and spread actions, while the encompassing action is carried out by adjusting the internal linkage. Based on the kinematic analysis and modeling of the proposed gripper, a prototype of the two-way adaptive gripper hardware was developed. Several experiments were performed to verify the feasibility and validity of the proposed gripper system. The actuator using the proposed differential gear was shown to be able to grasp objects in jammed conditions. In addition, the gripper was able to perform grasping actions, such as pinch, spread, and encompassing grasp.

The paper deals with the investigation of a workpiece moving unit with parallel kinematics. The subject of the study is the choice of the positions, installation location of actuator of the workpiece moving unit, table, how it affects the operation of the structure. This study is extremely important because the position of the actuators determines the functionality of the structure, i.e., we can predefine the position of the actuators so that the system can perform the desired movements. The possible installation locations of the actuators will be determined using combinatorics. Screw theory will be used to calculate the degree of freedom of the mechanism. [ABSTRACT FROM AUTHOR]

Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. In this study, first, according to the kinematics analysis of serial mechanisms, the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors. Then, based on the standard ideas of Lie operations, the method for kinematics analysis of parallel mechanisms is derived, and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form. Then, according to the mapping relationship between the parallel joints and corresponding equivalent series joints, a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined. A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example. The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible. [ABSTRACT FROM AUTHOR]

Singularity prediction of Jacobian is inherently related to the design of any manipulator. Optimization of Jacobian is known to improve the joint rates and joint torques for the same set of end-effector twists and wrenches. Any mathematical entity which is an estimator of Jacobian can be used as a manifestation of the stated two schemes. It is required that online computation of Jacobian be implemented so that singular poses can be avoided and performance is maximized. We present an algorithm that relates to the determinant of the Jacobian for robotic manipulators. The algorithm developed is quicker to compute, and a strategy is developed to synthesize the local estimator contour. The contours change dynamically, henceforth optimal motor torques (in case of presence of interaction fields or system requiring force control) and optimal joint rates can be defined, depending on the control algorithm. The algorithm developed is independent of the structure of the matrix and is generalized to any six DoF manipulator structure used. [ABSTRACT FROM AUTHOR]

This paper presents a three Degrees of Freedom (DOFs) parallel manipulator with no rotational capacity. Planar kinematic pairs (revolute joint and prismatic joint) are exclusively employed in this parallel structure. The parallelogram joint in each kinematic chain assists to ensure the moving platform's orientation is constant throughout the reachable workspace. Unlike the general parallel mechanisms, three identical kinematic limbs are degenerated to two kinematic limbs through merging two passive prismatic joints with same movement. Three active sliding joints are still required to drive this special parallel structure. Its mobility characteristic is firstly studied in detail and all possible singularity configurations are discussed by means of screw theory. The Lagrangian formulation is employed to compute the mathematical model of the inverse dynamic problem. The reachable workspace is obtained based on the inverse kinematic solutions. The distributions of the maximum joint force effect and maximum joint velocity effect are conducted. An example is provided to illustrate their trends under preset motion of the mobile platform. [ABSTRACT FROM AUTHOR]

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance. [ABSTRACT FROM AUTHOR]

This paper presents the type synthesis of 4-DOF non-overconstrained parallel mechanisms (PMs) with symmetrical structures. A special topological structure that includes two intermediate platforms and one moving platform is employed. Constraint conditions for 3R1T, 2R2T, and 1R3T (R: rotation; T: translation) symmetrical PMs are analyzed. Several classes of hybrid limbs that exert a constraint force or a constraint couple are synthesized using screw theory. These limbs are then used to construct 4-DOF PMs, resulting in many novel non-overconstrained 3R1T, 2R2T, and 1R3T PMs with symmetrical structures. The non-overconstrained feature is verified based on the Grübler/Kutzbach criterion.

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. [ABSTRACT FROM AUTHOR]

The paper presents novel models of reconfigurable parallel mechanisms (RPMs) with a single active degree-of-freedom (1-DOF). The mechanisms contain three to six identical kinematic chains, which provide three (for the tripod) to zero (for the hexapod) uncontrollable DOFs. Screw theory is applied to carry out mobility analysis and proves the existence of controllable and uncontrollable DOFs of these mechanisms. Each kinematic chain in the synthesized mechanisms consists of planar and spatial parts. Such a design provides them with reconfiguration capabilities even when the driving link is fixed. This allows reproduction of diverse output trajectories without using additional actuators. In this paper, the model of a mechanism with six kinematic chains (hexapod) has been virtually and physically prototyped. The designing and assembling algorithms are developed using the detailed computer-aided design (CAD) model, which was further used to carry out kinetostatic analysis considering complex geometry of mechanism elements and friction among all contacting surfaces of joints. The developed virtual prototype and its calculation data have been further applied to fabricate mechanism elements and assemble an actuated full-scale physical prototype for future testing. [ABSTRACT FROM AUTHOR]

It is crucial to perform volumetric error forward analyses of horizontal machining centers, including modeling, validation, and compensation, so that workpiece machining accuracies can be improved. Aiming at solving three major problems so far emerged in the machine tool volumetric error forward analyses, an integrated methodology is proposed in this paper. Firstly, in order to formulate a kinematic model without uncertainties and inconsistencies, a principle to determine the correct product relations of nominal motions to motion errors is systematically developed. Secondly, a novel validation approach based on the concept of volumetric vector Euclidean norm is demonstrated in this paper, assuring that the constructed volumetric error model can be quantitatively assessed without engaging any compensation processes. Thirdly, an optimal compensation technology is also presented to achieve the objective that the compensation residual errors, which are likely generated from the existing inverse superposition compensation strategies, can be diminished or even eliminated. A commercial horizontal machining center is selected to apply and verify the proposed integrated methodology. [ABSTRACT FROM AUTHOR]

SUMMARY: In this research, a dynamic model is first established based on screw theory and the principle of virtual work for a bilaterally symmetrical hybrid robot. By combining a novel composite error (NCE) with second-order nonsingular fast terminal sliding mode (SONFTSM) control method, a NCE-based SONFTSM dynamic control method is further presented to guarantee better trajectory tracking performance and synchronization performance simultaneously. The asymptotic convergence of proposed errors and the stability of the proposed control method have been proved theoretically. Finally, the simulation and experiment are implemented to validate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

The orientation ability and accuracy of parallel kinematic machines (PKMs) with two rotational and one translational outputs (2R1T) can be improved with the mechanical structures of 2R1T PKMs with limited degrees of freedom (DOF) limbs, fewer single-DOF joints, and no spherical joints. However, few existing 2R1T PKMs satisfy these conditions. This study proposes a new over-constrained 2UPR-PRU (where U, P, and R represent universal, actuated prismatic, and revolute joints, respectively) PKM with 2R1T DOFs with three limited-DOF limbs, no spherical joints, only 12 single-DOF joints, and one fixed motor. First, mobility, inverse displacement, and singularity analysis are carried out. Inverse dynamic models of the PKM are then established based on screw theory. Velocities, accelerations of limbs and moving platform, and actuation forces are derived. Simulation is carried out to verify the dynamic model, including the comparisons of actuation velocities, accelerations, and forces. Rotational and translational dynamic manipulability ellipsoid indices of the PKM in different operational heights are evaluated. The proposed PKM has good potential for machining work pieces with curved surfaces. [ABSTRACT FROM AUTHOR]

In order to improve the low structural strength of single-ring truss deployable mechanism with large aperture, a double-ring truss deployable mechanism (DRTDM) based on rectangular scissors unit is proposed, which has higher utilization rate and aperture expansion rate. First, the configuration of proposed DRTDM is analyzed and the size relationships between the components are derived. Then, the degree of freedom (DOF) of DRTDM is analyzed based on screw theory, and the results show that DRTDM has only one DOF. Through the displacement vector method and screw constraint topology, the velocity, acceleration and angular velocity of each component are obtained. Additionally, a dynamics model of the whole DRTDM is established based on Lagrange equation. Finally, above conclusions are verified by ADMAS simulation and the mobility of DRTDM is verified by the principle prototype. The DRTDM proposed in this paper provides a theoretical reference for the research and design of spatial deployable mechanism, and has potential value in the application of large aperture deployable mechanism. • A double-ring truss deployable mechanism is proposed. • DOF of the double-ring truss deployable mechanism is carried out by screw theory. • The kinematic model is established to show the deployable performance. • The dynamic characteristics are analyzed through Lagrange equation. • The theoretical analysis is verified by ADAMS and the principle prototype is built. [ABSTRACT FROM AUTHOR]

The dual quaternion plays an advantageous role in the field of robotic kinematics and dynamics due to its compact expression. It is well known that quaternion can be easily implemented as algebraic operations on vectors through matrix operators. Similarly, the dual matrix operators can convert dual quaternion operations to matrix operations. However, it has not received adequate attention, and thus there are very few applications at present. With the dual matrix operators of dual quaternion, this paper re-verifies the equivalency between the conjugate formula of unit dual quaternion and dual Euler–Rodrigues formula. To combine this equivalence with the homomorphic mapping of Lie groups, a theoretical correlation of the current hand-eye calibration methods is established. Motivated by the attempt to establish a more complete scheme for hand-eye calibration, a new simultaneous method based on the conjugate formula of dual quaternion is proposed. The method verifies that the rotation problem can be extended to the rigid-body transformation problem via the dual algebra. Finally, the simulation and experimental validations for the hand–eye calibration method are given. • The conjugate formula of unit dual quaternion is re-verified via the dual operations. • A new simultaneous method is defined for hand-eye calibration. • The theoretical correlation with the existing methods is established. [ABSTRACT FROM AUTHOR]

This paper presents a new solution for inverse kinematics (IK) by using dual quaternions (DQ) as operators and combining them with the Paden-Kahan subproblem to determine the analytical solution. Kinematics under the structure of screw theory makes the process mathematically efficient and gives geometric meaning. Both derived results and simulation outgrowths, when compared with the generally used numerical solution and matrix-based analytical solution, show that our method is faster and does not suffer from the numerical instability caused by being near to a singular configuration. The method has been proven to have the advantages of reducing the computational load and promoting precision, and it can provide multiple choices for IK.

A novel synchronous telescopic parallelogram mechanism with movement realized by a belt drive is proposed, from which a compound kinematic limb is derived. According to the configuration derivation, a class of two-translation (2T), three-translation (3T) and three-translation-one-rotation (3T1R) parallel mechanisms is obtained by assembling the above kinematic limbs. Since the motion of these limbs in the parallelogram mechanism are dependent, screw theory is applied to illustrate the mobility of the obtained lower mobility parallel mechanisms. Moreover, through the simplified kinematic equations for these mechanisms, their position, velocity and singularity are analyzed and their workspaces are calculated. Finally, the prototype of the 2T parallel mechanism is manufactured and experimented to validate mobility and motion feasibility.

Large diameter space deployable antenna is the key equipment for communication and data transmission between spacecraft and base stations on earth. Based on the overconstrained scissors mechanism, a double-hoop truss deployable antenna mechanism is constructed in this paper, which can be used as the antenna support mechanism for satellites and other spacecraft, and its kinematic characteristics and dynamics are analyzed based on screw theory. First, the configuration and the overconstrained features of the double-hoop truss deployable mechanism are analyzed with the truss mechanism divided into a plurality of mechanism units. The geometric conditions for the double-hoop form are also investigated with the consideration of joint size effects. Then, based on the screw theory, the degree of freedom (DOF) of the mechanism is analyzed, showing that this mechanism has only one DOF. Next, the velocity and acceleration of the components in the mechanism are examined. Through the screw and screw derivatives operation, the velocities and accelerations of the components and the Jacobian matrixes are obtained. Finally, a dynamic model of the double-hoop truss deployable mechanism is established based on the Newton-Euler equation and the principle of virtual work, and this model is verified by the numerical calculation and simulation verification. The overconstrained scissors double-hoop truss deployable antenna mechanism proposed in this paper has a good application prospect in the field of space deployable antennas, and the theoretical analysis method in this paper can provide insights into other complex spatial deployable mechanisms.

An accurate dynamic model is a prerequisite for realizing precise control of industrial robots. The dynamics research of multi-degree of freedom (DOF) robots is relatively unexplored and needs to be solved urgently. In this paper, a dynamic modeling method of multibody system of 6-DOF robot is proposed based on the screw theory. The established dynamic model has a more concise and unified mathematical form, and the modular matrix expression is convenient for the control of the robot. In order to ensure that the screw method is suitable for motion in a wide range of angles, quaternions are used as generalized angular coordinates, and the model established thereby eliminates singularities and improves computational efficiency. The correctness and accuracy of the screw method is verified by the simulation example, and the modeling theory and method can provide a theoretical basis for the precise control of the robot.

The Ilizarov external fixator plays an important role in the correction of complex malformed limbs. Our purpose in this work was to reveal the transmission of adjustable forces between the external fixator and the broken bone, and express the stress distribution at the end of the broken bone during the orthopedic treatment. Firstly, the screw model of the fixator was established and the theoretical relationship between the adjustable force and the stress was obtained. A sheep tibia was taken as a representative research object and its ediTable 3D entity was obtained by CT scanning. Then the mechanical model of the fixator and tibia was built using the ABAQUS software. Correction experiments were performed on the sheep tibia to measure the adjustable/support forces and tensions of the tibia. The measured results were imported to the screw and mechanical model, and the theoretical and simulation values were calculated. The theoretical tensions calculated by the screw model had a similar shape and doubled the value compared with that of the measured results. The transfer efficiency between the two results was improved and kept at about 50% after the initial 2~3 periods. The maximum stress occurring at the surface of the broken bone end was near the Kirschner wire pinhole. The simulation results for the tensions from the mechanical model showed a similar change trend, and the value was slightly higher. A biomechanical model of the Ilizarov external fixator was derived and verified through calculations, simulations and experiments. The change law of the adjustable forces and the tensions existing in the broken sheep tibias is presented herein, and offers a helpful contribution to orthopedic treatment.