Algebraic Method for Exact Synthesis of 1-DOF Linkages With Arbitrarily Prescribed Constant Velocity Ratios

This paper addresses the synthesis of 1-DOF linkages that can exactly transmit angular motion between coplanar axes (i.e. parallel axes or intersectant axes) with arbitrarily prescribed constant velocity ratios. According to motion polynomials over dual quaternions and pure rolling models between two circles, an algebraic approach is presented to precisely synthesize new 1-DOF linkages with arbitrarily prescribed constant velocity ratios. The approach includes four steps: (a) formulate a characteristic curve occurred by the pure rolling, (b) compute the motion polynomial of the minimal degree that can generate the curve, (c) deal with the factorization of the motion polynomial to construct an open chain, (d) convert the open chain to a 1-DOF linkage. Using this approach, several 1-DOF planar, spherical, and spatial linkages for angular motion transmission between parallel axes or intersectant ones are constructed by designating various velocity ratios. Taking the planar and spherical linkages with a constant 1:2 velocity ratio as examples, kinematics analysis is implemented to prove their motion characteristics. The result shows that the generated linkages indeed can transmit angular motion between two coplanar axes with constant velocity ratios. Meanwhile, 3D-printed prototypes of these linkages also demonstrate such a conclusion. This work provides a framework for synthesizing linkages that have great application potential to transmit motion in robotic systems that require low inertia to achieve reciprocating motion with high speed and accuracy.

A 3D-Printable Robotic Gripper Based on Thick Panel Origami

Origami has been a source of inspiration for the design of robots because it can be easily produced using 2D materials and its motions can be well quantified. However, most applications to date have utilised origami patterns for thin sheet materials with a negligible thickness. If the thickness of the material cannot be neglected, commonly known as the thick panel origami, the creases need to be redesigned. One approach is to place creases either on top or bottom surfaces of a sheet of finite thickness. As a result, spherical linkages in the zero-thickness origami are replaced by spatial linkages in the thick panel one, leading to a reduction in the overall degrees of freedom (DOFs). For instance, a waterbomb pattern for a zero-thickness sheet shows multiple DOFs while its thick panel counterpart has only one DOF, which significantly reduces the complexity of motion control. In this article, we present a robotic gripper derived from a unit that is based on the thick panel six-crease waterbomb origami. Four such units complete the gripper. Kinematically, each unit is a plane-symmetric Bricard linkage, and the gripper can be modelled as an assembly of Bricard linkages, giving it single mobility. A gripper prototype was made using 3D printing technology, and its motion was controlled by a set of tendons tied to a single motor. Detailed kinematic modelling was done, and experiments were carried out to characterise the gripper’s behaviours. The positions of the tips on the gripper, the actuation force on tendons, and the grasping force generated on objects were analysed and measured. The experimental results matched well with the analytical ones, and the repeated tests demonstrate that the concept is viable. Furthermore, we observed that the gripper was also capable of grasping non-symmetrical objects, and such performance is discussed in detail in the paper.

Design and Analysis of a Novel Reconfigurable Parallel Manipulator with Kirigami-inspired Bennett Plano-Spherical Linkages and Angular Pouch Motors

Drawing inspiration from kirigami, a creative art of papercutting, this paper first present a simple crease pattern of a kirigami model. In terms of artimimetics which bridges the origami/kirigami art and mechanisms, the kinematic equivalent, an overconstrained 6R linkage, is extracted from the kirigami model. In terms of screw theory, constraint singularity induced transitory position and distinct closed-loop motion branches of the 6R linkage is revealed. Using the Bennett plano-spherical linkage as a closed-loop subchain of kinematic limbs, this paper then introduce a new reconfigurable parallel manipulator with three hybrid kinematic limbs. Each limb of the manipulator consists of a Bennett plano-spherical linkage and a R(RR) serial chain. Using a geometric approach, the constraints exerted on the platform by the hybrid limb are explored by analysing the motion-screw systems of the equivalent serial kinematic limb corresponding to each motion branch of the closed-loop subchain. Motion characteristics in each motion branch of the parallel manipulator are revealed. Inspired by origami-folding and inflatable actuators for soft robotics, this paper further presents a new design of inflatable bending actuator for changing motion branches of reconfigurable mechanisms. The conceptual design of the actuator is verified with a prototype fabricated using adhesive fabric and further application in reconfiguring a 3D printed foldable Bennett plano-spherical linkage.

Clearance-induced orientation uncertainty of spherical linkages

This paper proposes a kinematic model to evaluate the orientation uncertainty range of spherical linkages caused by the joint clearances. Based on the concepts of imaginary clearance link, spherical N-bar rotatability laws, and the invariant link rotatability, the uncertainty of the output angle can be treated as a mobility problem. And the uncertainty region of the end-effector is treated as a workspace problem for the remodeled linkage. The paper highlights the orientation error by isolating the kinematic effects of joint clearance from other error factors. The discussion is carried out through spherical four-bar linkages and five-bar linkages. Numeric examples are presented to demonstrate the uncertainty range of the output angle and the uncertainty region of the end-effector. The result shows that, in the worst case, the error of each joint clearance will be magnified in a closed-loop structure compared with linearly adding all the clearance error. This implies that from a kinematics point of view, closed-loop spherical linkages or parallel manipulators will lead to a greater deviation on the end-effector than its open-loop counterpart. Using more passive joints in the manipulator may result in more error possibilities.

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line, and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

Optimization of a Spherical Decoupled Mechanism for Neuro-Endoscopy Based on Experimental Kinematic Data

ABSTRACTThe neuro-endoscopy is a surgical technique that allows the neurosurgeon to maintain a visual contact while operating inside the brain of a patient. A special instrument called the neuro-endoscope is inserted in the brain until the neurosurgeon reaches his/her target. Its manipulation requires a high level of training for neurosurgeons. To enforce both quality and safety of neuro-endoscopy, we propose a robotic manipulator based on a Spherical Decoupled Mechanism. This mechanical architecture has been modified from a 5-Bar Spherical Linkages and adapted to this medical application. It is able to generate a Remote Center of Motion of 2 Degrees of Freedom. It merges the advantages of parallel mechanisms with the kinematic and control simplicity of decoupled mechanisms, while having a very simple architecture. Motion capture experiments using a brain simulation model have been performed with a team of neurosurgeons to obtain the kinematic data of the neuro-endoscope during brain exploration. Based on the identified workspace, the mechanism has been optimized using kinematic performance and architectural compactness as criteria. An optimum mechanism has been selected, showing better kinematic performances than the original 5-bar spherical linkage mechanism.

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

Special Unitary Matrices in the Analysis and Synthesis of Spherical Linkages

This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved, and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.