The study of the relationship between the desired system dynamics and the actuation wrench producing those dynamics is important for robotic system analysis. For traditionally actuated robots, the quality indices of dexterity and manipulability quantify this relationship. However, for unilaterally actuated robots (UARs), such as grasping hands and cable-driven parallel robots (CDPRs), these indices cannot be applied due to the unilateral actuation constraint. In this paper, the quality indices of unilateral dexterity ( UD ) and unilateral maximum force amplification (UMFA) are established for UARs with arbitrary number of actuators. It is shown that these quality indices provide task-independent quantifications of the physical properties of robustness and force amplification for UARs, and they can measure the mechanism’s capability both in singular and nonsingular poses. With these indices, manipulability ellipsoid-derived measures can be applied to arbitrary UARs. The significance of the quality indices for robot synthesis and motion generation analysis is illustrated through two case studies: a five-fingered grasp selection problem and the workspace analysis of a spatial CDPR.

In this paper, a novel 3-UPU (P and U stand for prismatic and universal joints, respectively) parallel mechanism (PM) and its variant PM are proposed. Either of them has two rotational and one translational (2R1T) degrees of freedom (DOFs) and has no parasitic motion. The mobility analysis shows that three constraint forces provided by three limbs of the mechanism are located on the same plane and the mobile platform is capable of translating perpendicular to this plane and rotating around any axis on this plane. The motion characteristics of the mechanism are disclosed that the output motion of the mobile platform is only pure rotation or pure translation. And the rotation axis is constant during a rotation which means no parasitic motion. The reasons are analyzed and explained by the overall Jacobian matrix, statistical method and geometric method. Besides, it only needs to translate or rotate once to move from the initial configuration to the final configuration which facilitates the speed control. Then, the relationship between mechanism parameters and singularity is analyzed. At last, we proposed the speed control method for the PMs in this paper. And the prototype of the mechanism is manufactured. Then, the experiment is conduct that verifies the motion characteristics, the speed control method by overall Jacobian matrix and singularity.

A Jacobian-based topology optimization method is recently proposed for compliant parallel mechanisms (CPMs), in which the CPMs' Jacobian matrix and characteristic stiffness are optimized simultaneously to achieve kinematic and stiffness requirement, respectively. Lately, it is found that the characteristic stiffness fails to ensure a valid topology result in some particular cases. To solve this problem, an improved stiffness evaluation based on the definition of stiffness is adopted in this paper. This new stiffness evaluation is verified and compared with the characteristic stiffness by using several design examples. In addition, several typical benchmark problems (e.g., displacement inverter, amplifier, and redirector) are solved by using the Jacobian-based topology optimization method to show its general applicability.

Correct evaluation of robot performance has been a problem in the field of robotics. Many scholars have proposed a variety of performance indices, such as manipulability, condition number, and minimum singular value, to describe quantitatively the kinematic performance of a robotic mechanism. However, two questions remain: (1) how to describe the kinematic performance completely for the design of a robotic mechanism, and (2) how to comprehensively describe the global performance distribution characteristics in the workspace. This paper presents a global performance index system for kinematic optimization of a robotic mechanism based on Jacobian matrix, manipulability ellipsoid, and descriptive statistics theory that can comprehensively describe the kinematic performance and the performance distribution characteristics in a robot's workspace. First, the Jacobian matrix, a linear mapping from the joint space to the task space of a robotic mechanism, is analyzed, and the kinematic transmission ability indices and the kinematic transmission accuracy index are determined. Second, four indices, including global average value, global volatility, global skewness, and global kurtosis, are presented to describe the global performance index's distribution in the workspace. Third, the global performance index system is established to evaluate a robot's global kinematic performance based on the above analysis. Finally, a two-degrees of freedom (DOF) robotic mechanism is designed based on the global performance index system as a case, analysis of which shows that the final mechanism has good kinematic performance in the workspace. This demonstrates that the global performance index system proposed in this paper can be useful for the evaluation of the kinematic performance and kinematic optimization of a robotic mechanism.

Reconfigurable robotic systems can enhance productivity and save costs in the ever growing flexible manufacturing regime. In this work, the idea to synthesize robotic mechanisms with dynamic properties that are reconfigurable is studied, and a methodology to design reconfigurable mechanisms with this property is proposed, named reconfigurable dynamics (Re-Dyn). The resulting designs have not only the kinematic properties reconfigurable, such as link lengths, but also properties that directly affect the forces and accelerations, such as masses and inertias. A 2-degree of freedom (DOF) parallel robot is used as a test subject. It is analyzed and redesigned with Re-Dyn. This work also presents the robots forward dynamic model in detail, which includes the force balancing mediums. The connection method is directly utilized for this derivation, which is well suited for multibody dynamics and provides insight for design parameters (DPs). Dynamic performance indices are also briefly discussed as related to the Re-Dyn method. After redesigning the robot, a full simulation is conducted to compare performances related to a flexible manufacturing situation. This illustrates the advantages of the proposed method.

This paper addresses the kinematic analysis of a three-degree of freedom (DOF) compliant platform able to move in three dimensional space. The device is formed by the actuators, a central moving platform, and compliant joints. The actuators are three binary links. The moving platform is an equilateral plate. Springs connect the free end of each actuator with each vertex of the central platform. In this way, the motion of the actuators is transmitted to the moving platform. Compliant joints increase the complexity of the motion of the central platform and few studies have been carried out. This paper focuses on the forward and reverse analyses for the platform and the derivation of equations that relate the velocity of the moving platform with the velocity of the actuators.

Iterative algorithms are widely applied in reliability analysis and design optimization. Nevertheless, phenomena of failed convergence, such as periodic oscillation, bifurcation, and chaos, are oftentimes observed in iterative procedures of solving some nonlinear problems. In the present paper, the essential causes of numerical instabilities including periodic oscillation and chaos of iterative solutions are revealed by the eigenvalue-based stability analysis of iterative schemes. To understand and control these instabilities, the stability transformation method (STM), which is capable of tackling numerical instabilities of iterative algorithms in reliability analysis and design optimization, is proposed. Finally, several benchmark examples of convergence control of PMA (performance measure approach) for probabilistic analysis and the SORA (sequential optimization and reliability assessment) for reliability-based design optimization (RBDO) are presented. The observations from the benchmark examples indicate that the STM is a promising approach to achieve convergence control for iterative algorithms in reliability analysis and design optimization.

This paper investigates the behavior of a type of parallel mechanisms with a central strut. The mechanism is of lower mobility, redundantly actuated, and used for sprained ankle rehabilitation. Singularity and dexterity are investigated for this type of parallel mechanisms based on the Jacobian matrix in terms of rank deficiency and condition number, throughout the workspace. The nonredundant cases with three and two limbs are compared with the redundantly actuated case with three limbs. The analysis demonstrates the advantage of introducing the actuation redundancy to eliminate singularities and to improve dexterity and justifies the choice of the presented mechanism for ankle rehabilitation.

So far, in the derivation of the singularity equations of Gough–Stewart platforms, all researchers defined the mobile frame by making its origin coincide with the considered point on the platform. One problem can be that the obtained singularity equation contains too many geometric parameters and is not convenient for singularity analysis, especially not convenient for geometric optimization. Another problem can be that the obtained singularity equation cannot be used directly in practice. To solve these problems, this work presents a new approach to derive the singularity equation of the Gough–Stewart platform. The main point is that the origin of the mobile frame is separated from the considered point and chosen to coincide with a special point on the platform in order to minimize the geometric parameters defining the platform. Similarly, by defining a proper fixed frame, the geometric parameters defining the base can also be minimized. In this way, no matter which practical point of the platform is chosen as the considered point, the obtained singularity equation contains only a minimal set of geometric parameters and becomes a solid foundation for the geometric optimization based on singularity analysis.

This paper proposes an equivalent mechanism approach for establishing the stiffness matrices of some 3–5DOF (degree of freedom) parallel kinematic machines (PKMs) with S P ̱ R - or R P ̱ S -type legs and solving their elastic deformations. First, the geometric constraints of constrained wrench of these PKMs are analyzed, and the poses of the active/constrained forces are determined. Second, based on the principle of virtue work and the determined active/constrained forces, the formulas are derived for solving the 6 × 6 Jacobian matrices of these PKMs and the stiffness matrices of S P ̱ R or R P ̱ S -type active legs. Third, based on the elastic deformations of the S P ̱ R or R P ̱ S active legs, the equivalent 6-DOF rigid PKMs of these elastic PKMs are constructed, and their 6 × 6 Jacobian matrices are derived. Finally, the formulas are derived for solving the total stiffness matrices and the elastic deformation of the 3DOF 3 S P ̱ R , 3DOF 3 R P ̱ S , 4DOF 2 S P ̱ S + 2 S P ̱ R , and 5DOF 4 S P ̱ S + S P ̱ R PKMs.

Manufacturing techniques, especially in the microscale, determine the type of joints, links, and actuators available for the designer, and as a result, the possible kinematic architectures of the designed mechanism. This paper discusses the design constraints imposed by current microelectromechanical system (MEMS) fabrication techniques, and how they affect the feasible kinematic architectures of microrobots. In particular, three degree-of-freedom translational mechanisms are investigated, and all possible nonoverconstrained kinematic architectures under limitations imposed by MEMS fabrication techniques are derived.

This paper addresses optimal kinematic design and application of a redundantly actuated parallel manipulator with 3DOFs. Based on the kinematic model, the Jacobian matrix is derived and then transferred to a uniform form such that the conditioning index has explicit physical meaning. Based on the task workspace, the width between two columns is determined. Then, a comprehensive performance index, which compromises the conflict between workspace utilization performance measure and conditioning index, is proposed for the optimum design. The parallel manipulator is incorporated into a 4DOF hybrid machine tool, which also includes a feed worktable. Furthermore, a 5DOF machine tool is created by combining the parallel manipulator with a 2DOF worktable to machine blades of gas turbines.

In this paper, a 3-DOF 3-PRUR parallel mechanism (PM) is chosen for performance analysis and optimal design. First, the mobility of the PM is analyzed by using screw theory. Then, the kinematics of this PM is studied based on the geometrical characteristics and the Jacobian matrix is derived. Furthermore, we research some performance indices with respect to the Jacobian matrix over the whole workspace and nondimensional parameters when the input is given, and their performance atlases are obtained with different inputs. Finally, the optimal design of the PM is determined according to the performance atlases, and some examples are presented.

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3 - P ̱ RR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach.

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N -DoF ( N < 6 ) mechanism, this method can build a square ( N × N ) Jacobian matrix and cubic ( N × N × N ) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3- R ( C R R ) and 5-DoF 3- ( R R R ) ( R R ) are analyzed as examples.

The platform based vibratory bowl feeders are essential elements in automatic assembly. Taking the bowl feeder as a typical three-legged rigidly connected compliant platform device, this paper applies von Mises’ compliance matrix to each of the leaf-spring legs, establishes screw systems of the legs and develops the Jacobian of the platform using the adjoint transformation. Based on the force equilibrium between the supporting and external wrenches and the twist deflection, a platform compliance matrix is proposed as a congruence transformation of the legs’ compliance matrices. The matrix is then decomposed into a central compliance matrix and an adjoint transformation, leading to the decomposition of the legs’ parameter effect from the platform assembly influence. The analysis presents the necessary and sufficient condition for the existence of the twist deflection that is equivalent to the characteristics equation of the compliant platform. Further based on the eigencompliances and eigentwist decomposition, the legs’ parameter effect and the platform assembly parameter influence are identified. This reveals the compliance characteristics of this type of devices and the parameters’ effect on the compliance and presents a suitable parameter range for design of the compliant platform device.

Although the concepts of Jacobian matrix, manipulability, and condition number have existed since the very early beginning of robotics their real significance is not always well understood. In this paper we revisit these concepts for parallel robots as accuracy indices in view of optimal design. We first show that the usual Jacobian matrix derived from the input-output velocities equations may not be sufficient to analyze the positioning errors of the platform. We then examine the concept of manipulability and show that its classical interpretation is erroneous. We then consider various common local dexterity indices, most of which are based on the condition number of the Jacobian matrix. It is emphasized that even for a given robot in a particular pose there are a variety of condition numbers and that their values are not coherent between themselves but also with what we may expect from an accuracy index. Global conditioning indices are then examined. Apart from the problem of being based on the local accuracy indices that are questionable, there is a computational problem in their calculation that is neglected most of the time. Finally, we examine what other indices may be used for optimal design and show that their calculation is most challenging.

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables ( x , y , z , ϕ , θ , ψ ) , using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

It is a generally well-known fact that the design of parallel mechanisms while optimizing performance is quite difficult. In this paper, a reliable synthesis method capable of optimally selecting the geometrical parameters of planar parallel mechanisms is presented. Three different architectures are considered and a genetic algorithm is used to perform the optimization. The performance of each mechanism is evaluated according to four different criteria: workspace, singular configurations, dexterity, and stiffness. In order to make the synthesis method as realistic as possible, mechanical constraints affecting the angular rotation of the 2-R P ̱ R and 3-R P ̱ R mechanisms’ passive revolute joints are considered. Moreover, since the conventional methods for computing the dexterity and the stiffness index are not valid for the 3-R P ̱ R and 3- R ̱ RR mechanisms, an alternative computation method is used.