Bilateral teleoperation has witnessed significant development since the mid-20th century, addressing challenges related to human presence in environments with constraints or a lack of skilled professionals. This article presents the kinematic and self-collision analyses of the quasi-spherical parallel manipulator, a three-legged parallel robot used as a haptic master device. The device is designed for remote center of motion-constrained operation in the telesurgical field. Inverse and forward kinematics are thoroughly analyzed to study working modes, singular configurations, and implement a haptic control architecture. The research explores the operative and reachable workspaces of the possible working modes, comparing them to find the most suitable one. Results highlight how the addition of the self-collision phenomenon impacts the working mode choice, drastically reducing most of the modes’ operative workspaces. An anti-collision control algorithm is finally introduced to maintain the architecture within its reachable workspace.

Traction of the head-neck is important in the treatment of patients suffering from neck pain due to degeneration of the intervertebral discs. Conventional neck traction is provided manually by experienced physical therapists who maintain a desired orientation of the head-neck relative to the trunk while applying the traction. It is postulated that innovative designs of neck exoskeletons can provide the same function both flexibly and accurately. This article presents a novel architecture of a parallel mechanism whose base sits on the human shoulders with 4 parallel chains, each chain having a revolute-revolute-universal-revolute (RRUR) structure, while the end-effector is connected rigidly to the human head. Each chain has five degrees-of-freedom (DOF) and applies a constraint on the motion of the end-effector. As a result, this parallel mechanism allows two DOFs to the end-effector. These are (i) forward flexion or lateral bending of the head and (ii) vertical translation. An important motivation for the current design with RRUR structure is to characterize the range of forward flexion/lateral bending of the head-neck with this structure and the vertical translation to the end-effector. A physical prototype was constructed and tested to evaluate the performance of this mechanism in hardware for the proposed application.

Flexible cables in cable-driven parallel robots (CDPRs) are easy to be excited and vibrate. Cable vibration will react on the end-effector, causing attitude deviation of the end-effector. The main objective of this study is to accurately model axially moving flexible cables and characterize the dynamic behaviors of associated compliant CDPRs. Firstly, a model for transverse vibration of the axially moving length-variable cable is developed. On this basis, an original nonlinear dynamic model of the CDPRs able to capture the vibration of the cables and the dynamics of the end-effector is proposed. Secondly, the frequency–amplitude relationship of the CDPR is obtained. Moreover, the significance of the excitation effect caused by the axially moving length-variable cables is demonstrated, by comparing the results with and without excitation effect at different frequencies. It turns out that, as the oscillation frequency of the end-effector increases, the end-effector and cables exhibit the dynamics process from steady state to unstable large-amplitude vibration and finally to stable small-amplitude vibration. This indicates that the dynamics of the CDPR exhibit non-linear characteristics, due to the influence of flexible cables. Finally, the proposed dynamic model of compliant CDPRs is validated by experiments performed in the laboratory.

The axial offset joint has two rotating axes that do not intersect but have a specific offset in space. It is used widely in parallel manipulators (PMs). The offset-joint workspace can directly affect the PM workspace. This study performed a theoretical derivation and workspace analysis of a class of axial offset joints. First, a theoretical parametric model describing the rotation range of the offset joint is established that considers the interference of the offset joint because of the contact between the upper- and lower-joint brackets during movement. Second, the analytical expressions of the offset-joint workspace are formulated based on the coordinate system transformation. The offset-joint workspace is theoretically calculated in this study using formulations. Then, through a comparative analysis, the superiority of the offset joint compared with the universal joint is verified. The theoretical formulations in this paper can be used to calculate the workspace of a class of axial offset joints. Finally, based on a workspace analysis of three types of PMs using offset, universal, and spherical joints, the offset-joint PM workspace is much larger than those of the other two types.

As a heavy load is applied to the parallel manipulators, it causes inaccuracies while positioning the end-effector or unbalanced dynamic forces in the legs. Various load-balancing techniques overcome this. However, the disadvantage of most load-balancing mechanisms is that they add inertia to the assembly and decrease the speed of motion. This article studies a new load-balancing method (a passive damper mechanism). The passive balancing mechanism is proposed to negate the inertia effects while countering the static inaccuracies in the parallel mechanism. This is verified by the structural analysis of the mechanism. The impact of the damper element on the dynamics of the mechanism is unknown. Hence, a complete mathematical model for the balancing mechanism has been developed to study its impact on the dynamics of the entire structure. Laplace transformations characterize the system response. The inclusion of a passive damper in a 3-prismatic-prismatic-revolute-spherical system was examined and found to be stable and critically damped. Such a passive damper was envisaged to facilitate additional force transmission for the actuators, and the DC gain from the system response validates the torque support for the actuators.

This work addresses the gravity balancing of a 2R1T (2 rotations – 1 translation) mechanism with remote center of motion. A previously developed balancing solution is modified and applied to a prototype, and test results are presented. The mechanism is an endoscope holder for minimally invasive transnasal pituitary gland surgery. In this surgery, the endoscope is inserted through a nostril of the patient through a natural path to the pituitary gland. During the surgery, it is vital for the manipulator to be statically balanced so that in case of a motor failure, the patient is protected against any harmful motion of the endoscope. Additionally, static balancing takes the gravitational load from the actuators and hence facilitates the control of the mechanism. The mechanism is a 2URRR-URR type parallel manipulator with three legs. The payload mass is distributed to the legs on the sides. By using counter-masses for two links of each leg, the center of mass of each leg is lumped on the proximal link which simplifies the problem of balancing of a two degree-of-freedom inverted pendulum. The two proximal links with the lumped mass are statically balanced via springs. Dynamic simulations indicate that when the mechanism is statically balanced, generated actuator torques are reduced by 93.5%. Finally, the balancing solution is implemented on the prototype of the manipulator. The tests indicate that the manipulator is statically balanced within its task space when the actuators are disconnected. When the actuators are connected, the torque requirements decrease by about 37.8% with balancing.

During the movement of an optical mirror processing robot (OMPR), the movement error of each branch chain leads to contour errors of the grinding tool, which reduce the accuracy of the optical mirror surface. To improve the processing accuracy of an OMPR, it is necessary to study the control and compensation strategy of its contour error. In this study, first, a kinematics analysis of an OMPR is conducted, and the trajectory of the end execution point in the world coordinate system is transformed into the fixed coordinate system of the robot. Combined with the common trajectory of optical mirror processing, based on the Frenet coordinate system, contour error models of the OMPR in straight line, arc, and spiral trajectories are established. Subsequently, the contour error, feedforward channel gain, and compensation channel gain models of the parallel module are established in the task space, and concurrently, the control variables and stability of the system are analyzed. Finally, the established feedforward combined multi-axis cross-coupling contour control compensation strategy is analyzed experimentally to verify its accuracy and effectiveness. It provides a theoretical basis for a robot to directly face the precision processing object using the control and compensation strategy in a future research study to improve the molding accuracy of a surface and optimize the processing technology of a large-scale optical mirror.

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

This article discusses the intervertebral motion present in the craniovertebral junction (CVJ) region. The CVJ region is bounded by the first three vertebras from the spinal column. It helps in bringing most of the neck motion. Intervention in this region requires surgery in which an implant is placed to stabilize the whole system. The various available implants need to undergo performance evaluation as their performance varies from region and anatomical diversity. For the Indian population, we are targeting to evaluate the performance of such an implant, testing it into a cadaver. The region of interest will be loaded as per the loading condition of an average human. Motion in these regions is evaluated using the camera. A preliminary test was done on a saw bone model of CVJ to assess the performance of segmentation methods. Multiple such ArUco markers are used to increase pose accuracy further, and the pose of the entire board of multiple tags provides us with reliable pose estimation. The absolute error ranged from a minimum of 0.1 mm to a maximum of 16 mm. At the same time, the mean and median absolute errors were 3.8961 mm and 3.35 mm. By considering the absolute lengths, the percentage error showed the following trends. The percentage error was between 3.9168% and 0.0230%.

In this study, several joint axis orientations on equilateral platforms and the limbs of 3-UPU parallel manipulators (PMs) are examined. The generated joint layouts for the platforms were matched with each other to generate and enumerate manipulator architectures based on certain assumptions. The structures of thus obtained manipulators are examined and limb types were determined. These limb types were analyzed using screw theory. The instantaneous mobility of the manipulators and the motion characteristics of the moving platforms are tabulated. The finite mobility analysis of one of the manipulators is performed using a software package as an example. Among several different 3-UPU PM architectures, 118 novel 3-UPU PMs with non-parasitic 3-degrees-of-freedom are significantly important. The classified 3-UPU PMs with determined motion characteristics can be used by researchers as a design alternative for their specific design task.

This paper presents the design and simulation of a Parallel Kinematic (PK) testbed for head impacts. The proposed design is presented as a novel head impact testbed using a parallel platform as main motion simulation mechanism. The testbed is used to give a motion to a head mannequin to impact against a steel plate. In addition, the platform in the testbed allows to modify the orientation of the head mannequin model to evaluate different types of impacts. The testbed has been modeled with software MS ADAMS® to evaluate its performance with a dynamic simulation and to characterize the testbed design during top and lateral impact events. Results show that PK testbed gives a significant force and acceleration to the head mannequin at the moment of the impact.

To overcome the physical limitations of mechanical bone cutting in minimally invasive surgery, we are developing a miniature parallel robot that enables positioning of a pulsed laser with an accuracy below 0.25 mm and minimizes the required manipulation space above the target tissue. This paper presents the design, control, device characteristics, functional testing, and performance evaluation of the robot. The performance of the robot was evaluated within the scope of a path-following experiment. The required accuracy for continuous cuts was achieved and reached 0.176 mm on the test bench.

This paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

The topological structure of a parallel manipulator (PM) determines its intrinsic topological properties (TPs). The TPs further determine essential kinematic and dynamic properties of the mechanism. TPs can be expressed through topological characteristics indexes (TCI). Therefore, defining a set of TCIs is an important issue to evaluate the TPs of PMs. This article addresses the evaluation of topological properties (ETP) of PMs based on TCI. A general and effective ETP method for PMs is proposed. Firstly, 12 TCIs are proposed, including 8 quantitative TCIs, that is, position and orientation characteristics sets (POC), dimension of the POC set, degrees of freedom (DOF), number of independent displacement equations, types and number of an Assur kinematic chain (AKC), coupling degrees of the AKCs, degrees of redundancy and the number of overs; as well as 4 qualitative TCIs, that is, selection of actuated joints, identification of inactive joints, DOF type and Input–Output motion decoupling. Secondly, the ETP method is illustrated by evaluating some well-known PMs including the Delta, Tricept, Exechon, Z3, H4 and the Gough–Stewart platform manipulators, as well as 28 other typical PMs. Via the ETP analysis of these mechanisms also some valuable design knowledge is derived and guidelines for the design of PMs are established. Finally, a 5-DOF decoupled hybrid spraying robot is developed by applying the design knowledge and the design guidelines derived from the ETP analysis.

People with severe neuromuscular trunk impairment cannot maintain or control upright posture of the upper body in sitting while reaching. Passive orthoses are clinically available to provide support and promote the use of upper extremities in this population. However, these orthoses only position the torso passively without any degree of trunk movement.

We introduce for the first time a novel active-assistive torso brace called Wheelchair Robot for Active Postural Support (WRAPS). It consists of two rings over the hips and chest connected by a 2RPS-2UPS parallel robotic device. WRAPS can modulate the displacement of the upper ring and/or the forces applied on the torso through the ring in four degrees-of-freedom (DOF), including rotations and translation in the sagittal and frontal planes.

In the present study, we evaluate the design of WRAPS and its functions. Moreover, we discuss the potential effectiveness of WRAPS as a therapeutic robotic tool in people with severe trunk control deficits. The performance of WRAPS was evaluated in seated healthy subjects. Kinematics and surface electromyography (sEMG) were collected when the participants performed selective trunk movements. First, the torso range of motion (tROM) was calculated with WRAPS in transparent mode—zero-force control mode—which was compared with free-guided tROM (no WRAPS) with motion capture system. Second, a position control mode was configured to mobilize the torso along the trajectories obtained with the transparent mode.

Our results show that the design of WRAPS suited well the subject’s anthropometrics while supporting the weight of the torso. Importantly, WRAPS can be programmed to replicate the subject’s tROM, without the full activation of torso muscles. This can be critical in individuals with no trunk control. Altogether, these preliminary results indicate the potential applicability of WRAPS to promote active-assistive trunk mobility in people who cannot sit independently because of trunk dysfunction.

In this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

Parallel manipulators, especially those with outputs as one translation and two rotations (1T2R), are being increasingly studied. The kinematic chains of parallel manipulators share the loads and make the stiffness higher than the stiffness of serial manipulators with equivalent limbs. This high stiffness ensures a minimal deformation of the limbs, allowing a high positioning accuracy of the endeffector. Thus, it is very important to be able to measure the stiffness in parallel manipulators. In this work, we present a novel 1T2R multi-axial shaking table (MAST) for automobile pieces testing purposes—the 2PRU–1PRS parallel manipulator—and focus on the analysis of its stiffness all over the useful workspace. Analysis methods based on matrix structural method need to be validated for every parallel manipulator, and we present these steps along with a comparison between experimental and analytical methods.

This paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.

Singularity analysis of parallel manipulators is an active research field in robotics. The present article derives for the first time in the literature a condition under which a five-bar parallel robot encounters high-order parallel singularities. In this regard, by focusing on the planar 5R mechanism, a theorem is given in terms of the slope of its coupler curve at the parallel singular configurations. At high-order parallel singularities, the associated determinant vanishes simultaneously with at least its first-order time derivative. The determination of such singularities is quite important since in their presence, some special conditions should be satisfied for bounded inverse dynamic solutions.

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 2PRPU 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.