The 4-DOF (four degrees of freedom) parallel manipulator, namely 2PPaRR-2PPaRU, offers three translations and one rotation capabilities, boasting an extensive rotation range, and a regular workspace. Moreover, its workspace can infinitely extend in conjunction with the extension of the driving joints. Nonetheless, the symmetric structure relying on Pa joint design presents performance challenges in the initial configuration and complicates the analytical solution of the forward kinematics, thereby increasing the complexity of dynamics and control. To address these limitations, the structure of the moving platform is modified by coaxially connecting the three joints at the ends of the three limbs to the moving platform. This improvement is followed by analyses of mobility, motion/force transmissibility, and stiffness. The overall reachable workspace area, good transmission workspace ratio, and global stiffness index are then chosen as key objectives for dimensional optimization, thereby achieving satisfactory performance for the new 3T1R PM. Finally, the CAD model with the selected parameters is presented, together with the distributions of motion/force transmission index and virtual stiffness index within the reachable workspace. The results validate the effectiveness of the optimization design.

In this article, the performance analysis and multiobjective structure optimization of 4RRR parallel mechanism are carried out. Firstly, the 4RRR pure rotation parallel mechanism and its design route are introduced. Secondly, the Jacobian matrices in 2DoF pure rotation and 3DoF pure rotation modes are derived using the motion equations of the mechanism. Next, the singularity analysis, kinematic dexterity analysis, dynamic dexterity analysis, and stiffness analysis of the mechanism are carried out, respectively, and it is proved that there is no singularity in the mechanism in its workspace. Since the dexterity performance expression is a nonlinear piecewise function, the kinematic local comprehensive dexterity index and the dynamic local comprehensive dexterity index are proposed as the objects of analysis. Furthermore, the kinematic global comprehensive dexterity index, the dynamic global comprehensive dexterity index, and the global comprehensive stiffness index are proposed to carry out the multiobjective structural optimization. Finally, NSGA3 was used to complete the optimization, and the comprehensive optimal solution of the structure size was obtained.

Cable-guiding mechanisms (CGMs) and the stiffness characteristics directly influence the dynamic features of the cable-driven upper limb rehabilitation robot (PCUR), which will affect PCUR’s performance. This paper introduces a novel CGM design. Given the precision and movement stability considerations of the mechanism, an analytical model is developed. Using this model, we analyze the error of the CGM and derive velocity and acceleration mappings from the moving platform to the cables. Continuity of cable trajectory and tension is rigorously demonstrated. Subsequently, a mathematical model for PCUR stiffness is formulated. Utilizing MATLAB/Simscape Multibody, simulation models for the CGM and stiffness characteristics are constructed. The feasibility of the proposed CGM design is validated through simulation and experimentation, while the influence of stiffness characteristics on PCUR motion stability is comprehensively analyzed.

This paper presents an eight wire-driven parallel robot (WDPR-8) designed to serve as a suspension manipulator for aircraft models during wind tunnel testing. The precision of these tests is significantly influenced by the system’s stability and workspace, both of which are shaped by the geometric configuration of the structure and the tension in the wires. To acquire the efficiency principle of the suspension scheme design for the model, a kinematics model for a WDPR-8 was established. Based on the kinematics model, the stiffness of a WDPR-8 was theoretically studied, and the analytical expression of stiffness matrix of a WDPR was deduced. The stiffness matrix was composed of two terms, one of which is determined by the configuration of suspension system and the other term is determined by the wire tension. Based on the analysis result, a set of suspension scheme was discussed under the calculation of stiffness matrix and workspace analysis. In the discussion process, in addition to the stiffness-maximum calculation, another criterion as force closure is presented, which is useful for increasing the stiffness and workspace of the robot. Finally, a prototype was established according to the analysis result, and the workspace experiments are conducted. Test results indicate that the workspace meets the design requirements, validating the system suspension design method of a WDPR for aircraft model suspension in wind tunnel test considering of the systematic stiffness and workspace.

This paper proposes a new antagonistic tendon-driven joint (TDJ) that exhibits higher stiffness and larger travel range than conventional types of TDJs. A detailed mathematical analysis of the stiffness of the proposed TDJ is conducted and compared to other TDJs. The effect of the tendon length is taken into consideration to establish a more precise and realistic stiffness model of the proposed TDJ. Thereafter, two hardware prototypes of the proposed TDJ design, developed in the form of a packaged modular structure that integrates two TDJs, are introduced. Using these prototypes, the stiffness characteristics of the proposed TDJs are verified through experimentation. Additionally, experimental results on the stiffness behavior during the mimicked needle insertion tasks are provided. Results show that the proposed TDJs present much higher stiffness than conventional ones and thus give a potential benefit to precision manipulation.

This paper deals with the stiffness analysis of multibody systems using the Matrix Structural Analysis—MSA. This methodology allows us to obtain the stiffness matrix of the structure from the stiffness properties of each element. First the MSA method is described and its application is detailed using an L-structure in order to make easy its understanding. Numerical and experimental results obtained for the L-structure and a 6-RSS parallel manipulator, follow to prove the validity of the methodology.

A redundantly actuated parallel kinematic machine (PKM) can be used to avoid singularities, normalize manipulability, and increase the stiffness of anon-redundant mechanism. In this study, a redundantly actuated symmetrical PKM with five revolute (5R) joints is optimized for isotropic stiffness in the workspace. The stiffness of the 5R symmetrical PKM is calculated by the superposition of the actuator stiffness and the structural stiffness. We compared the stiffness of anon-redundant PKM and a redundant PKM. Compliance ellipses of the actuator stiffness and the structural stiffness of the non-redundant PKM resulted in the same configurations in the workspace, while those of the redundant PKM resulted in very different configurations. Optimization was performed by determining the optimal actuator torques that are needed to maximize the conditioning index. Optimal results considering structural stiffness can provide a more uniform directional stiffness than optimal results considering the index. When the strength of the linkages in a PKM is weak, the structural stiffness affects the actual stiffness considerably. We believe that the results of this study can be used to help design and control redundant PKMs.

A novel parallel hip joint simulator, called 3SPS+1PS bionic parallel test platform, with 4 degrees of freedom including three rotations and one translation is designed to represent three-dimensional motion and compound friction movement of a human hip joint and to be a better simulator for testing the tribology performance of biomaterials for hip joint prosthesis. Stiffness is one of the most important performances of parallel manipulators, as well as for the 3SPS+1PS parallel manipulator with higher speeds. First, the differential kinematic/static model was derived based on the kinematics model. The relationship between the elastic deformation of each active leg and the variation of position/orientation deformation of the moving platform was described based on the virtual work principle. Then, a 6 × 6 global stiffness matrix of the 3SPS+1PS parallel manipulator was derived. The maximum versus minimum eigenvalues of the global stiffness matrix were obtained as its two evaluation indexes. By letting the 3SPS+1PS bionic parallel test platform represent three rotation motions and the dynamic loading of the human hip joint as described by ISO 14242 Part-1, the forces acted on each active leg and their responding elastic deformations were analyzed. The distributions for maximum and minimum stiffness in different workspace were detected. Finally, the results showed that the minimum stiffness in the whole workspace should be larger than the allowable stiffness of the 3SPS+1PS parallel manipulator.

This paper presents a new methodology for the joint stiffness identification of industrial serial robots and as consequence for the evaluation of both translational and rotational displacements of the robot's end-effector subject to an external wrench (force and torque). In this paper, the robot's links are supposed to be quite stiffer than the actuated joints as it is usually the case with industrial serial robots. The robustness of the identification method and the sensitivity of the results to measurement errors, and the number of experimental tests are also analyzed. The Kuka KR240-2 robot is used as an illustrative example throughout the paper.

In this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663–676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global conditioning index (GCI) of the manipulator is calculated and compared with another SPM. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. A continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano's theorem. The mathematical model is verified by finite element model. Finally, using mathematical model, kinematics stiffness index (KSI), and global stiffness index (GSI) are evaluated.

In our previous work, we developed a compact 6-DOF haptic interface as a master device which achieved an effective manual teleoperation. The haptic interface contains a modified Delta parallel-link positioning mechanism. Parallel mechanisms are usually characterized by a high stiffness, which, however, is reduced by elastic deformations of both parts and bearings. Therefore, to design such a parallel mechanism, we should analyze its structural stiffness, including elastic deformations of both parts and bearings. Then we propose a simple method to analyze structural stiffness in a parallel mechanism using bearings. Our method is based on standard concepts such as static elastic deformations. However, the important aspect of our method is the manner in which we combine these concepts and how we obtain the value of the elasticity coefficient of a rotation axis in a bearing. Finally, we design a modified Delta mechanism, with a well-balanced stiffness, based on our method of stiffness analysis.

In this paper a hybrid parallel-serial manipulator, named as CaHyMan (Cassino Hybrid Manipulator), is analyzed in term of stiffness characteristics as a specific example of a general procedure for analyzing stiffness of parallel-serial manipulators. A formulation is presented to deduce the stiffness matrix as a function of the most important stiffness and design parameters of the mechanical design. A formulation is proposed for a stiffness performance index by using the obtained stiffness matrix. A numerical investigation has been carried out on the effects of design parameters and fundamental results are discussed in the paper.