Robot Mechanics

This paper concerns kinematics and dimensional synthesis of a three universal-revolute-universal (3-URU) pure rotational parallel mechanism. The mechanism is composed of a base, a platform and three symmetric limbs consisting of U-R-U joints. This mechanism is a spatial non-overconstrained mechanism with three degrees of freedom. The joints in each limb are so arranged to perform pure rotational motion of the platform around a specific point. Equations for inverse displacement analysis and singularities were derived to investigate the relationship of the kinematic constants to the solution of the inverse kinematics and singularities. Based on the results, a dimensional synthesis procedure for the 3-URU parallel mechanism considering singularities and the workspace was proposed. A numerical example was also presented to illustrate the synthesis method.

The direct kinematics problem of parallel mechanisms, that is, determining the pose of the manipulator platform from the linear actuators’ lengths, is, in general, uniquely not solvable. For this reason, instead of measuring the lengths of the linear actuators, we propose measuring their orientations and, in most cases, also the orientation of the manipulator platform. This allows the design of a low-cost sensor system for parallel mechanisms that completely renounces length measurements and provides a unique solution of their direct kinematics.

A six-degree of freedom (DOF) two-radii Gough-Stewart Platform (GSP) can be designed to be dynamically isotropic and has been proposed for micro-vibration isolation. In many applications, the torsional mode can be ignored, and a 5-DOF dynamically isotropic, parallel manipulator capable of attenuating three translational (3T) and two rotational (2R) modes are sufficient. In this work, we present the designs of a novel 5-DOF dynamically isotropic parallel manipulator for vibration isolation where the torsion mode can be ignored. We present closed-form solutions in their explicit form, and these are obtained using a geometry-based approach. The first design is based on a modification to the two radii GSP and provides enhanced design flexibility and feasibility. The second design, with the first five decoupled modes, is based on superposing geometrical parameters of two 3-legged dynamically isotropic or decoupled parallel manipulators. It is shown that this design has two translational modes, namely the X, Y modes, which are decoupled from two rotational modes Rot(X), Rot(Y) and are controlled by two different sets of three legs. This feature can lead

Computing joint commands in real time by solving an inverse kinematic (IK) problem is an important manipulation task that is commonly encountered in agricultural operations such as fruit harvesting, disease detection and leaf sampling. To date, different numerical and analytical approaches have been proposed, and many of them are able to take constraints into account. In this study, a set of analytical algorithms is investigated to quickly solve the constrained five-degree-of-freedom inverse kinematic problem. The constraints due to actuator limitations and mechanical design of the mechanism are utilised in generating the solution sets for joint variables. Also a suboptimal solution for the inverse kinematic problem within this set is derived. The proposed methods are compared with a typical numerical solution based on non-linear constrained optimisation. It is shown that the proposed analytical and suboptimal semi-analytical solutions can be found in a much quicker fashion as compa...

A typical parallel mechanism (PM) consists of a moving platform connected to a fixed base by means of several kinematic chains, called legs. Only some kinematic pairs are actuated, in number generally equal to the number n of degrees of freedom (dofs) that the platform possesses with respect to the base; the other joints are passive. Usually, the number of legs is also equal to n. This makes it possible to actuate only one pair per leg, allowing all motors to be mounted close to the base. Such mechanisms show desirable characteristics like a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. With respect to serial manipulators, disadvantages are a lower dexterity, a smaller workspace and more serious consequences caused by kinematic singularities (which are configurations in which the functioning of the mechanism is disrupted). Since their first designs [1, 2], 6-dof PMs have been extensively studied, whilst only in relatively recent times have manipulators with fewer dofs attracted researchers' attention. As they are potentially architecturally simpler and cheaper than their 6-dof counterparts (they require less parts and actuators), their use may be advantageous in all those applications in which less than six dofs are required. Different architectures of 3-dof mechanisms have been presented in the literature. Depending on the kind of motion exhibited by the platform, PMs can be divided into: • mixed (MPMs); • spherical (SPMs); • translational (TPMs). The first allow the platform to both translate and rotate and may be employed as motion simulators, wrists of hybrid serial-parallel robots and mixed orienting/positioning systems [3-7]. The second enable the travelling plate to rotate about a fixed point and may be used in those applications that require orienting a body in space, be it a solar panel, an antenna, a telescope, a gun, the end-effector of a robot, a human or humanoid artificial limb, etc. [8-18]. The last provide the output link with a pure translational motion and may be particularly valuable in the fields of automated assembly and machine tools as • deprive the platform of one or more dofs of rotation, so that, by virtue of the contribution of all legs, platform turning is completely prevented; • be consistent with a 3-dof translational motion of the platform.

Many procedures to detect singularities in manipulators have been described in the literature up to now. Singularities are often defined as an instantaneous or permanent modification in the number of degrees of freedom (DOF), either affecting certain links or the whole mechanism. However, the motion of the end-effector of a parallel manipulator is not only given by the number of DOF but also by the nature of them (rotational or translational). There are poses in which, being no quantitative alteration of the DOF of the platform, there are changes in this nature. This is also a singularity, and produces, as other singularities do, a mathematical deficiency in the velocity equations of the manipulator. This type of singularity affects only the so called lower mobility parallel manipulators. In this contribution the authors define this new type of singularity, called motion pattern singularity, and present a procedure to analyze it.

Combining human and robot into a particular structure put forward extraordinary opportunities for generating a new generation of knowledge. The idea of producing a mechanism that can strictly collaborate with humans. This advance spot presents innovative challenges for engineers and designers. On the contrary, to industrial robotics meant for which mechanical stiffness and rigidity, accuracy and high velocities are most important requirements the solution feature. Here is a movement freedom that matches to that of the human people, avoidance of risk to users and a lightweight mechanism. In order to achieve these requirements the robot should have a human like appearance, same workspace, dexterity and the kinematics should be common to the user. This article presents a new design of a robotic arm wrist for the next development of humanoid robots, and it is a part of an ongoing project that involves a 7-DOF robotic arm powered by electrical actuators and has a new hybrid structure. The aim of this research is to achieve a human like wrist that has the same number of degree of freedom and improves the workspace. The new mechanism of the wrist is discussed in details in the article.

This paper studies the singularity of a four-limb parallel robot of SCARA motion. The robot is designed with the rotation axis of the mobile platform parallel to the base platform, which allows the robot to be mounted vertically, instead of the horizontal installation, to reduce the mounting space. The singularity is analyzed by means of Jacobian-based pressure angles, which are applicable for the singularity identification graphically and numerically. Moreover, the index defined from the pressure angles can be used to evaluate the motion/force transmission quality of the robot. The singularity loci of the wall-mounted robot with specific parameters are identified, which shows that the robot has a large cuboid singularity-free translational workspace with rotational capability ±45 • , suitable for pick-and-place operations.

In this paper, an innovative Reconfigurable Spherical Motion Generator (RSMG) is introduced to provide continuous spherical motion and force transmission. The mechanism enables unlimited workspace in 3-DOF spherical motion with rapid, continuous and precise motion capability. The conceptual design, as well as direct and inverse kinematics, are presented here. Singularities of the mechanism are analyzed. An actuation strategy is proposed such that the RSMG is capable of avoiding any types of singularities in order to produce unlimited spherical motion.

A mechanism with redundant constraints can present some aligning problems due to manufacturing inaccuracies. Tolerances are commonly used by designers to avoid this kind of problem. This papers apply the knowledge of self-aligning mechanisms and modern analysis tools to propose a method to distribute clearances in the project of mechanisms, this is useful to avoid alignment problems. The self-aligning approach employs Davies' method and Matroid theory. The overconstrained mechanism of a commercial hospital bed is evaluated and the tolerances are then discussed to achieve a mechanism without aligning problems.

In this paper, we present the mechanical design of a spherical four-bar mechanism for performing a motion common in manufacturing and assembly processes. The mechanism is designed to create, in a single, smooth motion, the combined rotation of a body by 90 degrees about one axis with a 90 degree rotation about an axis perpendicular to the first. A spherical four-bar mechanism is pursued as the basis for the design because the reorientation is produced mechanically rather than via a control scheme typical when higher degree of freedom systems are utilized. The design initiates with the kinematic synthesis of the spherical mechanism to guide a body through two orientations. The next step in the design is to refine the spherical fourbar based on manufacturing and operational concerns. As one of the challenges of utilizing these four-bars is tuning the starting and ending angle for the mechanism’s motion, a sensitivity analysis is performed to gauge the needed accuracy. Finally, there a...

This paper presented a parallel robotic manipulator having combined DOF, i.e., one translational and two rotational DOF, called PRoM-120. PRoM-120 is constructed by using 2PRU/PRS kinematic chains (KCs) and arranged in an asymmetric configuration. The objective of the research is to determine the workspace and to evaluate the performance of PRoM-120 for three cases based on the numerical values of its kinematic constants. The workspace is calculated by applying the discretization method. The inverse kinematic solution, direct singularity, inverse singularity, and actuators limit are taken as the significant factor to determine the workspace. Meanwhile, the performance of PRoM-120 is evaluated by applying conditioning index and transmission based index. It shows the conditioning index cannot be used for PRoM-120, or parallel manipulator having combined DOF. Assessing the performance of PRoM-120 using transmission based index exposes only less than 20% of the workspace be in the good ...

In this paper, our goal is to improve angular resolution of 77 GHz radar with eight receiver channel by using a multi-radar system and high-resolution direction-of-arrival (DoA) estimation algorithm. The theoretical and experimental results show that angular resolution can be improved 42.6% with multi-radar system compared to a single radar system when two targets have exact the same distances from the radar. In this paper, we also show experimental studies for forward backward spatial smoothing (FBSS) multiple signal classification (MUSIC) DoA estimation algorithm. The algorithm is demonstrated in a real world indoor environment and the results of the estimated DoAs showed considerably good agreement with the predicted angles. By using this algorithm, angular resolution can be improved 40.8% compared to fast Fourier transform (FFT) beamforming (BF) algorithm.

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.

This letter has supplementary downloadable material available at http:// ieeexplore.ieee.org, provided by the author. The Supplemental Materials contain a video comparing the workspace of the proposed joint to that of human joints, showing the possibility of an almost-complete coverage by the device workspace, which is limited only by kinematic singularities. This material is 18.3 MB in size.

Only one parallel wrist with three equal legs containing just revolute pairs has been already presented in the literature. This parallel wrist is overconstrained, i.e., it involves three degrees of freedom required to orientate the end effector by using repetitions of constraints. The overconstrained mechanisms have the drawback of jamming or undergoing high internal loads when geometric errors occur. This paper presents a new parallel wrist, named 3-RUU wrist. The 3-RUU wrist is not overconstrained. It has three equal legs just involving revolute pairs and actuators adjacent to the frame and uses an architecture (3-RUU) already employed to obtain manipulators that make the end effector translate. The 3-RUU wrist kinematic analysis is addressed. This analysis shows that the new parallel wrist can reach singular configurations (translation singularities) in which the spherical constraint between end effector and frame fails. The singularity condition that makes finding all the 3-RUU ...

Differently from previously presented underactuated parallel wrists (PWs), RU-(nS)PU 2 wrists feature a single-loop architecture and only one nonholonomic constraint. The presence of a nonholonomic constraint makes these PWs underactuated: they are able to control the platform orientation in a three-dimensional workspace by employing only two actuated pairs, one prismatic (P) and the other revolute (R), but they cannot perform tracking tasks. Their position analysis, path planning, and kinetostatics are studied. All their relevant position-analysis problems are solved in closed form, and, based on these closed-form solutions, a path-planning algorithm is built. Their instantaneous kinematics and singularity analysis are addressed, too: all their singular configurations are identified through analytic and geometric conditions, whose static interpretation is given. The presented results are relevant for designing this type of underactuated PWs.

Combining human and robot into a particular structure put forward extraordinary opportunities for generating a new generation of knowledge. The idea of producing a mechanism that can strictly collaborate with humans. This advance spot presents innovative challenges for engineers and designers. On the contrary, to industrial robotics meant for which mechanical stiffness and rigidity, accuracy and high velocities are most important requirements the solution feature. Here is a movement freedom that matches to that of the human people, avoidance of risk to users and a lightweight mechanism. In order to achieve these requirements the robot should have a human like appearance, same workspace, dexterity and the kinematics should be common to the user. This article presents a new design of a robotic arm wrist for the next development of humanoid robots, and it is a part of an ongoing project that involves a 7-DOF robotic arm powered by electrical actuators and has a new hybrid structure. The aim of this research is to achieve a human like wrist that has the same number of degree of freedom and improves the workspace. The new mechanism of the wrist is discussed in details in the article.

In general, a rigid body moving in space can possess three translational and three rotational degrees-offreedom. In many situations, the motion of the rigid body is constrained, and therefore has less than six-degrees-offreedom. In such cases, it is often important to understand how the degrees-of-freedom are distributed between pure translation and pure rotation. In this paper, we present a general approach towards the partitioning of the available instantaneous degrees-of-freedom for the constrained motion of rigid-bodies. The approach is based on computing the eigenvalues and eigenvectors of certain matrices associated with the instantaneous motion of a rigid body. The eigenvalue problem involves the solution of at most a cubic polynomial, and hence the eigenvalues can be obtained in closed form in all the cases. The approach is applied to several well known three-degrees-of-freedom spatial parallel manipulators. It is well-known that parallel manipulator can gain one or more degrees-of-freedom at a gain-type singularity. The general approach is also applied to determine if the gained degree(s)-of-freedom are in translational or rotational in nature.

While significant progress had been made in synthetic biology over the last decade, researchers still lack a reliable tool for computeraided design of gene regulatory networks (GRN), one that can reveal the full range of nonlinear dynamic behaviors in a single run. Here, we propose a network design cycle that utilizes both the qualitative simulation of GRNs modeled by a class of ODE equations and the intrinsic stochasticity of regulation to ultimately design a network that exhibits a specified desired behavior with the highest probability. Finally, to show the power and ease of our method, we perform a case study with a real-life benchmark gene network to get a synthetic oscillator.

Singularities of the configuration space for planar parallel mechanisms involving prismatic joint are investigated using a kinematic constraint map approach. Eliminating pose parameters from the singularity conditions together with the constraint equations leads to Grashoftype conditions. We illustrate the method by the planar RRRP and 3-RPR parallel mechanisms. In the latter case, conditions for higher order singularities are also determined.

A reverse analysis of a 6 degree of freedom (dof) subchain of a modified 7 dof flight telerobotic servicer (FTS) manipulator system is presented. The 6 dof subchain is designated as a TR-RT* chain. At the outset, it was considered that the reverse analysis would be similar to a TTT manipulator analyzed previously for which the third and fourth joints intersect at a finite point. This was not, however, the case and a sixteenthdegree tan-half-angle polynomial was derived for the TR-RT manipulator. The elimination procedure is interesting and much simpler than the procedures for the general case. *This abbreviation describes the sequence of manipulator joints beginning with the first grounded hook joint (universal joint) T. The sequence R-R designates a pair of revolute joints with parallel axes.

An efficient reverse analysis of three 6‐degree‐of‐freedom (dof) subchains of the 7‐dof SSRMS is presented. The first subchain is formed by locking the seventh joint. The second subchain is formed by locking the second joint, while the third subchain is formed by locking the first joint (the grounded joint is counted as the first joint in the chain). There are a maximum of eight different arm configurations in each of the three subchains, and these were determined by employing a computer‐efficient algorithm, which required the rooting of only at most quadratic polynomials. The algorithms were implemented, and the SSRMS was employed in an animated environment to perform and practice a number of useful tasks for space station servicing. The locking of the second joint has the advantage in that an operator could, at the outset, choose the orientation of the plane that contains the two longest links (the upper arm and forearm) so as to avoid collisions with obstacles. However, it has th...

A 4-DOF over-constrained RRPU + 2UPU parallel manipulator (PM) with 3 legs is proposed, and its kinematics, statics, workspace, and singularity are studied systematically. First, the structure constraints and DOF (degree of freedom) of this PM are analyzed; and the geometric constrained equations are derived. Second, some analytic formulae are derived for solving the inverse/forward displacements, velocities, accelerations, active forces and torque of this PM. Third, a reachable workspace of this PM is constructed and analyzed. Finally, some analytic solutions are given and verified by its simulation mechanism.

This paper presents synthesis methods and performance measures for wire-actuated wrists using a universal-joint constraining linkage. Performance measures based on the isotropy of the wrench-closure workspace are derived and used in generating design atlases as a function of non-dimensional design parameters. The performance indices that are optimized include wrench-closure workspace, isotropy of the wrench-closure workspace, and kinematic conditioning index. Stiffness is used to define a safety margin from singularities of wrench closure. A design example of a wireactuated surgical wrist is presented and validated through simulation. The methods presented in this paper are useful for quick dimensional synthesis of wire-actuated wrists with predefined wrench-closure workspaces.

This paper presents synthesis methods and performance measures for wire-actuated wrists using a universal-joint constraining linkage. Performance measures based on the isotropy of the wrench-closure workspace are derived and used in generating design atlases as a function of non-dimensional design parameters. The performance indices that are optimized include wrench-closure workspace, isotropy of the wrench-closure workspace, and kinematic conditioning index. Stiffness is used to define a safety margin from singularities of wrench closure. A design example of a wireactuated surgical wrist is presented and validated through simulation. The methods presented in this paper are useful for quick dimensional synthesis of wire-actuated wrists with predefined wrench-closure workspaces.

Lower mobility parallel manipulators are designed to perform tasks that require less than six degrees of freedom. The operational mode is given by the type of screw system spanned by the end-effector's twist and it is configuration dependent. A change in the dimension of such screw system occurs at singularities; a loss of freedom of the end-effector will make the operation not feasible while a gain of freedom will produce uncontrolled motions. In this contribution the authors show that there are also poses in which, being no quantitative alteration of the freedom of the moving platform, there are changes in the type of its screw system. These changes are viewed as transitions in the velocity pattern of the end-effector. Such transitions can alter the operational motion and produce a problem that should be avoided, but it can be also a useful new operational mode. Because in many industrial applications the operational mode is viewed in terms of the pure translations and the rotations available in the end-effector, the authors have used such concepts to denote the type of motion. In this paper the authors present a procedure to analyze these transitions and present an example.

The static analysis of a parallel wrist, known as the 3-universal-prismatic-universal (UPU) wrist, is presented, and the 3-UPU wrist singularity conditions are interpreted from a statics point of view. An equation (singularity equation) that enables finding all the 3-UPU wrist singular configurations is written in explicit form. Moreover, the use of the Rodrigues parameters to parameterize the 3-UPU wrist platform orientation allows the singularity equation to become a fourth-degree polynomial equation in three unknowns. Finally, a numerical example is presented.

Manipulators with 3-RSR topology are three-degree-of-freedom parallel manipulators that may be either spherical or mixed-motion manipulators. The inverse position analysis (IPA) and the workspace determination of 3-RSR manipulators are addressed by means of a new approach. The new approach is centered on a particular form of the closure equations called compatibility equations. The compatibility equations contain only the six coordinates (end-effector coordinates) which locates the end-effector pose (position and orientation) with respect to the frame, and the geometric constants of the manipulator. When the manipulator geometry is assigned, the common solutions of the compatibility equations are the end-effector coordinates which identify the end-effector poses belonging to the manipulator workspace. Moreover, they can be the starting point to easily solve the IPA. The presented compatibility equations can be also used to solve the position synthesis of the 3-RSR manipulator. This ...

Parallel manipulators are constituted of two rigid bodies, one movable platform and Ž. Ž. the other fixed base , connected by a number of kinematic chains legs. Manipulators with all equal legs that have the actuators adjacent to the base allow the use of simplified design procedures and manufacturing processes. Moreover, they are able to reach high performances. Further manufacturing simplifications can be obtained if only revolute pairs and passive cylindrical pairs are used. This article presents a new spherical parallel manipulator, named the 3-URC wrist. The 3-URC wrist is not overconstrained. It has three equal legs having only passive cylindrical pairs and revolute pairs with the actuators adjacent to the base. The 3-URC wrist mounting and manufacturing conditions making spherical motions of the platform possible are defined. Then the position analysis and the mobility analysis of the 3-URC wrist are solved. Finally, the singularity conditions are written in explicit form and geometrically interpreted.

This paper presents robotic manipulators that employ the bevel gravity compensator. The bevel gravity compensator can counterbalance a 2-dof rotation comprised of two 1-dof gravity compensators and a bevel differential. Each 1-dof gravity compensator is equipped at the rotating bevel gear, respectively. Analyses of the energy and torque for a 1-link and 2-dof manipulator indicate that the proposed gravity compensator performs static balancing completely. Multi-link and spatial manipulator applications are discussed in this paper. In these applications, mechanical constraints are adopted to achieve complete gravity compensation, since the pose of the distal link with respect to the inertial frame varies with alterations of the pose of the proximal link. Energy analyses reveal that the proposed manipulators employing bevel gravity compensators can completely achieve static balancing. The simulation results show that the gravitational torques can be effectively counterbalanced in regards to the proposed manipulators.

In this paper, we present the mechanical design of a spherical four-bar mechanism for performing a motion common in manufacturing and assembly processes. The mechanism is designed to create, in a single, smooth motion, the combined rotation of a body by 90 degrees about one axis with a 90 degree rotation about an axis perpendicular to the first. A spherical four-bar mechanism is pursued as the basis for the design because the reorientation is produced mechanically rather than via a control scheme typical when higher degree of freedom systems are utilized. The design initiates with the kinematic synthesis of the spherical mechanism to guide a body through two orientations. The next step in the design is to refine the spherical fourbar based on manufacturing and operational concerns. As one of the challenges of utilizing these four-bars is tuning the starting and ending angle for the mechanism’s motion, a sensitivity analysis is performed to gauge the needed accuracy. Finally, there a...

Ces travaux de thèse apportent plusieurs contributions à la conception de dispositifs d'assistance robotisés pour la réalisation de procédures d'insertion d'aiguille sous imageur à rayons X. Partant de la tâche de positionnement et d'orientation d'une aiguille, plusieurs architectures mécaniques inédites à quatre degrés de liberté ont été proposées. Un algorithme de synthèse dimensionnelle a été conçu pour calculer les paramètres structuraux de ces mécanismes en étudiant leurs singularités, tout en tenant compte des contraintes antagonistes de compacité du système, de capacité d'actionnement et de taille d'espace de travail. Une décomposition modulaire du dispositif d'assistance a permis de proposer des solutions pour un outil dédié à l'insertion d'aiguille avec retour d'effort. Cet outil comporte un dispositif d'insertion, un système de préhension d'aiguille et un capteur d'effort spécifique pour le retour d'effort.This th...

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.

This paper presents two types of five-degree-of-freedom parallel mechanism generating 3T2R motion with linear inputs. The kinematic geometry of the mechanism is presented and several important kinematic issues including the inverse kinematic problem, the velocity equations and the constant orientation workspace are investigated. The main contribution of this work is the determination of the workspace using Bohemian domes. This approach provides a 3D solid model that can be built in any CAD system.

During chest compressions action, in CPR (CPR), the 2 arms of the rescuer constitute a parallel mechanism. Inspired by this performance, during this study a specific family of lower mobility parallel manipulators by employing a modified version of Delta robot is proposed for chest compressions in rescuing a patient. One of the biggest differences between this mechanism and the Delta parallel mechanism is that the position of the three active connections of the robot relative to each other has changed the geometry of the platforms. Also, it shapes the asymmetrical structure within the robot mechanism and its workspace. Another difference is due to the architectural optimization method considering the mixed performance index, which has been used during this mechanism to achieve a much better compromise between the manipulator dexterity and its workspace. Within the present paper, after introducing the architecture of the robot, a closed-form solution is developed for the kinematic pro...

This paper presents a new approach to calculate the direct and inverse differential kinematics for serial manipulators. The approach is an extension of the Davies method for open kinematic chains based on a virtual kinematic chain concept introduced in this paper. It is a systematic method that unifies the kinematics of serial manipulators considering the type of kinematics and the coordinate system of the operational space and constitutes an alternative way to solve the differential kinematics for manipulators. The usefulness of the method is illustrated by applying it to an industrial robot.

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The dimensional synthesis of translational parallel manipulators (TPMs) of type PRRR-PRPU is addressed by using an overall novel method. Addressing this design step on such TPMs is interesting for the scientific community since, in a previous paper, one of the authors showed that it has the following promising features: a single-loop not-overconstrained architecture with all the actuators on or near to the base, a simple position analysis, easy-to-find workspace boundaries, no constraint singularity, a type-II singularity locus that is a plane easy to keep far from the useful workspace, and a double infinity of isotropic configurations. The presented synthesis includes the analysis of isotropy and dexterity by local and global conditioning indexes, the useful workspace optimization, and the accuracy and stiffness analyses. The result is the identification of a normalized TPM of type PRRR-PRPU with performances that are comparable with those of commercial TPMs. The identified normalized TPM yields a set of actual TPMs with the same performances by changing the value of a reference geometric length. Also, the chosen shape of the useful workspace (i.e., a cuboid) matches the needs of many industrial applications.

A mechanism with redundant constraints can present some aligning problems due to manufacturing inaccuracies. Tolerances are commonly used by designers to avoid this kind of problem. This papers apply the knowledge of self-aligning mechanisms and modern analysis tools to propose a method to distribute clearances in the project of mechanisms, this is useful to avoid alignment problems. The self-aligning approach employs Davies' method and Matroid theory. The overconstrained mechanism of a commercial hospital bed is evaluated and the tolerances are then discussed to achieve a mechanism without aligning problems.

The type synthesis is a fundamental phase in the design of parallel mechanisms. The type synthesis process consists of a systematic approach to generate all possible mechanical structures that are capable of performing a determined movement. The type synthesis presents two main steps: (1) generation of limbs and (2) assembly of parallel manipulators. There are basically three main approaches for type synthesis of parallel mechanisms: screw theory, lie group of rigid body displacements and evolutionary morphology. This paper presents a new method that combines screw theory and characteristics of genetic algorithms. Using the proposed method, it was generated new solutions of 3-DOF limbs (2R1T and 1R2T) for parallel manipulators.

This paper presents a novel asymmetric parallel mechanism with three degrees of freedom, with properties of self-aligning called Triflex II. Triflex II is composed of three legs: PRRR þ PRRU þ PRRS that connect a moving platform to the base. This paper discusses the properties of asymmetry and selfaligning of the mechanism presenting and discussing the complete analytical mathematical modeling of direct and inverse kinematics of position and velocity, using geometrical approaches. It is presented also a study of singularities and workspace limits. In order to validate the developed kinematic modeling a numerical simulation is presented. Keywords 3-DOF parallel mechanism Á Selfaligning Á Asymmetrical kinematic chain Á Forward and inverse kinematics

A new decoupled 3D translational pantograph manipulator with symmetrical design is proposed. Since its three linear actuators are placed on/near the base, it possesses, to some extent, the advantages of parallel manipulators such as high speed, high stiffness and high accuracy. Since its structure is close to that of serial manipulators, its workspace to size ratio is high, comparable to that of serial manipulators. Moreover, the end-effector of the proposed manipulator has decoupled translation motions in three perpendicular directions with fixed orientation. Also, the manipulator has a linear input/output relationship for the positioning problem. Other possible architectures for the proposed manipulator are presented where the manipulator can have 4, 5 or 6 DOFs. The unconventional interconnected structure of the proposed manipulator does not allow the use of known mobility analysis methods. So, a novel method based on sketching the 3D velocity diagram is developed to derive the full-cycle mobility for general (serial, parallel or interconnected) manipulators. The kinematics, workspace, singularity and stiffness of the proposed manipulator are studied. The results show that the proposed manipulator outperforms the known translational decoupled Pantopteron manipulator regarding the workspace to size ratio. The proposed manipulator can also achieve configuration-independent and near-isotropic behaviors.