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The article discusses the importance of motion and kinematics in the field of robotics. It highlights how robots have become a part of everyday life and are reshaping society in various fields. Kinematics plays a central role in the design of robotic systems, covering topics such as mechanism analysis and synthesis, robot control, path planning, and bioinspired robotics. The article also mentions the "Kinematics and Robot Design" (KaRD) series, which provides a platform for scientists to present and discuss new ideas and applications in an open science setting. The sixth edition of KaRD, published in 2023, included ten papers on topics such as mechanism synthesis, geometric error effects, medical robotics, and robot control. The article concludes by acknowledging the members of the KaRD series' Scientific Committee. [Extracted from the article]

In a planar mechanism, the position of the instant centers reveals important pieces of information about its static and kinematic behaviors. Such pieces of information are useful for designing the mechanism. Unfortunately, when the mechanism architecture becomes complex, common methods to locate the instant centers, which are based on the direct application of the Aronold-Kennedy theorem, fail Indeterminate linkages are single-degree-of-freedom (single-dof) planar linkages where the secondary instant centers cannot be found by direct application of the Aronold-Kennedy theorem. This paper presents an analytical method to locate all the instant centers of any single-dof planar mechanism, which, in particular, succeeds in determining the instant centers of indeterminate linkages. In order to illustrate the proposed method, it will be applied to locate the secondary instant centers of the double butterfly linkage and of the single flier eight-bar linkage. [DOI: 10.1115/1.2839008] Keywords: single-dof planar mechanism, indeterminate linkage, double butterfly linkage, single flier eight-bar linkage, primary instant centers, secondary instant centers

A wide family of parallel manipulators (PMs) is the one that groups all PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen. Keywords: Kinematics, Position Analysis, Parallel Mechanisms, Parallel Structure

The use of less than six degrees of freedom (dof) mechanisms instead of six-dof ones is always recommended when the application makes it possible, since their architectures and control are simpler to manufacture and implement respectively. Three-dof mechanisms constitute an important subset of less-than-six-dof mechanisms, since either translational or spherical motion can be obtained through three-dof spatial mechanisms and many industrial applications require the only translational or spherical motion. This paper presents a new translational parallel mechanism (TPM), named translational 3-URC. The new mechanism belongs to the parallel architectures with 3-URC topology, which contain another architecture that is a spherical parallel wrist. The proposed TPM is not overconstrained and has three equal legs whose kinematic pairs are three revolute pairs and one passive cylindrical pair per leg. Its actuated pairs are three revolute pair located on the frame. The position and velocity analyses of the translational 3-URC will be addressed and solved. Its singularity conditions will be written in explicit form and geometrically interpreted. [DOI: 10.1115/1.1814390]

Orientating a rigid body without changing its position is required in many technical applications. This manipulation task is accomplished by manipulators (spherical manipulators) that are just able to make the end effector move according to controlled spherical motions. Spherical manipulators can be either serial or parallel. Parallel architectures are usually more stiff and precise than the serial ones, whereas their structures are more complex than the serial ones. This paper presents a new three-equal-legged spherical parallel manipulator, named the 3-RRS wrist. The 3-RRS wrist is not overconstrained and exhibits a simple architecture employing just three passive revolute pairs, three passive spherical pairs and three actuated revolute pairs adjacent to the frame. The kinematic analysis of the 3-RRS wrist is addressed and fully solved. Finally its singularity conditions are written in explicit form and discussed. The results of this analysis lead to the conclusion that the new manipulator has only two types of singularities both easy to he identified with geometric reasoning. [DOI: 10.1115/1.1767819]

Among the new architectures for parallel wrists, recently presented in the literature, one of the simplest is the architecture of the 3-revolute-spherical-revolute (RSR) wrist. The kinematics of the 3-RSR wrist has not been presented yet, in the literature. This paper presents the kinematic analysis of the 3-RSR wrist. In particular, the demonstration that the 3-RSR wrist makes the end-effector perform finite spherical motion is reconsidered from a different point of view. The new demonstration directly provides the constraint singularities of the 3-RSR wrist. Moreover, the position analysis of the 3-RSR wrist is reduced to the solution of problems already solved in the literature. Finally, the mobility analysis of the 3-RSR wrist is addressed, and all its singularity conditions are found in analytical form and geometrically interpreted. Index Terms--Kinematics, parallel manipulators, wrist.

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. Index Terms--Parallel wrists (PWs), robotics, singularity loci, statics.

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (limbs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. This paper studies the singular geometries both of the PS-2RS structure and of the 2PS-RS structure. In particular, the singularity conditions of the two structures will be written in a new form. This new form will directly bring to a new geometric interpretation of their singularity conditions and to the exhaustive enumeration of the geometric conditions identifying their singular geometries. Such an enumeration will reveal that some geometric conditions were not identified in the literature. Finally, the use of the obtained results in the design of parallel manipulators which become either PS-2RS or 2PS-RS structures, when the actuators are locked, will be illustrated. [DOI: 10.1115/1.1758251]

This paper presents a dynamic model of parallel wrists with all links constrained to have a spherical motion with the same center. The model can also be applied to serial wrists. The model, based on Lagrangian formulation of dynamics, exploits the feature that all the links have the same fixed point. Three parameters defining the platform orientation are used as generalized coordinates. This choice allows the use of the generalized inertia matrix (GIM) appearing in the model to calculate effective dynamic performance indices proposed in a previous paper. The model can solve both the direct and the inverse dynamic problems. It also contains the Jacobian matrix useful to characterize the kinematic behavior of parallel manipulators. By the model it is shown that the best performances are reached in the workspace regions where the manipulator has a good kinematic and dynamic isotropy, whereas the incidence of nonlinear forces on performances is relevant at high end-effector speed. A numerical example is provided.

The occurrence of singular configurations in parallel mechanisms must be avoided during motion since the actuators cannot control motion even in the neighborhood of these configurations. As a consequence, the knowledge of the singular configurations of the mechanism is important for control purposes, for singularity-free path planning, and also represents basic information for the synthesis of a desired mechanism workspace free from singularities. In this paper the mobility analysis of the 3-UPU parallel mechanism assembled for obtaining a pure translation motion of the output platform is performed and both translation and rotation singularity loci are presented in analytic form and their geometric interpretation is given. [DOI: 10.1115/1.1471530] Keywords: Parallel Manipulators, Mobility Analysis, Singularity, Pure Translational Motion

SUMMARY: Pick-and-place applications need to perform rigid body displacements that combine translations along three independent directions and rotations around one fixed direction (Schoenflies motions). Such displacements constitute a four-dimensional (4-D) subgroup (Schoenflies subgroup) of the 6-D displacement group. The four-degrees of freedom (dof) manipulators whose end effector performs only Schoenflies motions are named Schoenflies-motion generators (SMGs). The most known SMGs are the serial robots named SCARA. In the literature, parallel manipulators (PMs) have also been proposed as SMGs. Here, a novel single-loop SMG of type 2 P R P U is studied. Its position analysis, singularity loci and workspace are addressed to provide simple analytic and geometric tools that are useful for the design. The proposed single-loop SMG is not overconstrained, its actuators are on or near the base and its end effector can perform a complete rotation. These features solve the main drawbacks that parallel SMG architectures have in general and make the proposed SMG a valid design alternative. [ABSTRACT FROM AUTHOR]

In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to nonlinear equations that are difficult to solve. In particular, the inverse position analysis comprises different subproblems which need specific solution techniques. Finally a numerical example is reported. [DOI: 10.1115/1.1324670]

It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to five out of the six sensors normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure. [S1050-0472(00)01703-7]

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. [ABSTRACT FROM AUTHOR]