Accepted Manuscripts

Design Innovation Paper  
Zeljko Situm and Petar Trslic
J. Mechanisms Robotics   doi: 10.1115/1.4040490
The paper presents the results of modeling and control of an original and unique ball-on-beam system with a pneumatic artificial muscle pair in an antagonistic configuration. This system represents a class of under-actuated, high-order nonlinear systems, which are characterized by an open-loop unstable equilibrium point. Since pneumatic muscles have elastic, nonlinear characteristics, they are more difficult to control. Considering that, an additional non-linearity is added to the system which makes it harder to stabilize. The nonlinear mathematical model has been derived based on the physical model of the ball-on-beam mechanism, the beam rotating by using an antagonistic muscle pair and the pneumatic muscle actuated by a proportional valve. Based on the nonlinear model, the linearized equations of motion have been derived and a control-oriented model has been developed, which is used in the state feedback controller design procedure. The proposed state feedback controller has been verified by means of computer simulations and experimentally on the laboratory setup. The simulation and experimental results have shown that the state feedback controller can stabilize the ball-on-beam system around an equilibrium position in the presence of external disturbances and to track a reference trajectory with a small tracking error.
TOPICS: Muscle, State feedback, Control equipment, Equilibrium (Physics), Equations of motion, Trajectories (Physics), Design, Nonlinear systems, Errors, Computer simulation, Simulation, Proportional valves, Control modeling
Ting-Li Yang, Anxin Liu, Hui-Ping Shen, Lu-Bin Hang and Qiaode Jeffrey Ge
J. Mechanisms Robotics   doi: 10.1115/1.4040488
Based on the general DOF formula for spatial mechanisms proposed by the author in 2012, the early SOC-based composition principle for planar mechanisms is extended to general spatial mechanisms in this paper. Firstly, three types of existing mechanism composistion principle and their characteristics are briefly discussed. Then the SOC-based composition principle for general spatial mechanisms is introduced. According to this composition principle, a spatial mechanism is firstly decomposed into AKCs and an AKC is then further decomposed into a group of ordered SOCs. Kinematic (dynamic) analysis of a spatial mechanism can then be reduced to kenamatic (dynamic) analysis of AKCs and finally to kinematic (dynamic) analysis of ordered SOCs. The general procedure for decomposing the mechanism into ordered SOCs and the general method for determining AKC(s) contained in the mechanism are also given. Mechanism's kinematic (dynamic) analysis can be reduced
TOPICS: Kinematics, Chain
Long Kang, Wheekuk Kim and Byung-Ju Yi
J. Mechanisms Robotics   doi: 10.1115/1.4040462
This paper introduces a family of statically balanced 5-DOF parallel mechanisms with kinematic and actuation redundancy. Moving platforms of this family of parallel mechanisms can provide 4-DOF Schönflies motion. Three applications are considered in this work. The first and second applications use kinematic redundancy to avoid parallel singularities and perform an auxiliary grasping task in sequence. The third application incorporates actuation redundancy into a kinematically redundant manipulator to increase the load-carrying capacity. Screw theory was used to derive the Jacobian of the 5-DOF parallel mechanism with kinematic and actuation redundancy. Parallel singularities can be completely alleviated by controlling the orientation of the redundant link, thereby obtaining a large rotational workspace, and actuation redundancy increases the load-carrying capacity. Using a commercially available multibody dynamic simulator, an example of trajectory was performed to illustrate the large rotational workspace of the first and second applications and compare the Euclidean norm of the vector of actuation torque of non-redundant and redundant parallel mechanisms. Three prototypes were also developed to demonstrate the output motion and static balancing property.
TOPICS: Kinematics, Redundancy (Engineering), Modeling, Parallel mechanisms, Load bearing capacity, Trajectories (Physics), Grasping, Torque, Screws, Engineering prototypes, Jacobian matrices, Redundant manipulators
Robert Read
J. Mechanisms Robotics   doi: 10.1115/1.4040433
The Boerdijk-Coxeter helix (BC helix, or tetrahelix) is a face-to-face stack of regular tetrahedra forming a helical column. Treating the edges of these tetrahedra as structural members creates an attractive and inherently rigid space frame, and therefore is interesting to architects, mechanical engineers, and roboticists. A formula is developed that matches the visually apparent helices forming the outer rails of the BC helix. This formula is generalized to a formula convenient to designers. Formulae for computing the parameters that give proven edge-length minimaxoptimal tetrahelices are given, allowing transformation through a continuum of of optimum tetrahelices of varying curvature while maximizing regularity. The endpoints of this continuum are the BC helix and a structure of zero curvature, the equitetrabeam. Only one out of three members in the system change their length to transform the structure into any point in the continuum. Numerically finding the rail angle from the equation for pitch allows optimal tetrahelices of any pitch to be designed. An interactive tool for such design and experimentation is provided: https://pubinv.github.io/tetrahelix/. A formula for the inradius of optimal tetrahelices is given. The continuum allows a regular Tetrobot supporting a length change of less than 16% in the BC configuration to untwist into a hexapodal or n-podal robot to use standard gaits.
TOPICS: Robots, Mechanical engineers, Architects, Structural elements (Construction), Space frame structures, Design, Rails
Ming Li and Wei Cheng
J. Mechanisms Robotics   doi: 10.1115/1.4040437
This paper presents the design and experimental validation of a novel type of passive large-displacement constant-force mechanism (CFM). Unlike previous studies, without using extra stiffness-compensation components and active control devices, the CFMs designed in this paper utilize the interaction between the components of cam and sliders to directly achieve the constant-force characteristic over the entire flexible-designed large displacement once the cam is advisably designed with profile curve identification method (PCIM). Corresponding to the different requirements of conventional and extreme engineering environments, the basic and ultra large-displacement CFM models are proposed respectively. The basic model is directly based on the PCIM while the ultra-large-displacement model is proposed using the relay-action of the multi-stage sliders. Friction factor is considered in the design theory to improve the accuracy and engineering applicability of the CFMs. According to the theoretical design models, we design and fabricate two corresponding CFM prototypes. Validation experiments are then conducted and the results show that both of the prototypes can satisfy the design requirements and possess the large-displacement constant-force characteristics due to the consistency of experimental and design data. Therefore, the effectiveness of the design theory for large-displacement CFM design is validated and the designed CFMs will have extensive applications in the relevant fields for force regulation and overload protection.
TOPICS: Design, Displacement, Design theory, Engineering prototypes, Friction, Stiffness
Huijuan Feng, Rui Peng, Jiayao Ma and Yan Chen
J. Mechanisms Robotics   doi: 10.1115/1.4040439
Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the pre-determined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist pattern using the kinematic equivalence between rigid origami and spherical linkages. All schemes of M-V assignment were derived based on the flat foldable conditions, among which rigidly foldable ones were identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard were developed by applying kirigami technique to the rigidly foldable pattern without changing its degree of freedom. The proposed method opens up a new way to generate spatial overconstrained linkage from the network of spherical linkages. It can be readily extended to other types of origami patterns.
TOPICS: Linkages, Degrees of freedom, Engineering systems and industry applications, Kinematics
Technical Brief  
Zhirui Wang, Yaobin Tian and Yanan Yao
J. Mechanisms Robotics   doi: 10.1115/1.4040438
This paper presents a novel underactuated tetrahedral mobile robot with twelve degrees of freedom (DOFs). The robot contains four vertices and six URU chains (where U represents a universal joint, R represents an actuated revolute joint). The tetrahedral structure makes the robot have continuous mobile ability at any posture. The mobility analysis has been made and demonstrates the feasibility of underactuated which demands fewer devices and low costs. A kind of rolling locomotion of the robot is proposed and the feasibility of the locomotion is proved by the kinematic and locomotion analysis based on an equivalent planar mechanism. Finally, a prototype is manufactured and a series of experiments are performed to verify the mobile capability of the robot.
TOPICS: Mobile robots, Robots, Universal joints, Engineering prototypes, Degrees of freedom, Chain, Mechanical admittance, Kinematics
Jingchen Hu and Tianshu Wang
J. Mechanisms Robotics   doi: 10.1115/1.4040435
This paper presents a method to minimize the base attitude disturbance of a space robot during target capture. First, a general dynamic model of a free-floating space robot capturing a target is established using Spatial Operators, and a simple analytical formula for the base angular velocity change during the impact phase is obtained. Compared with former models proposed in the literature, this model has a simpler form, a wider range of applications and O(n) computation complexity. Second, based on the orthogonal projection matrix lemma, we propose the Generalized Mass Jacobian Matrix and find that the base angular velocity change during the impact phase is a constant times the orthogonal projection of the impact impulse on the column space of the Generalized Mass Jacobian Matrix. Finally, a new concept, of the Base Attitude Disturbance Ellipsoid, is proposed to express the relationship between the base attitude disturbance and the impact direction. The impact direction satisfying the minimum base attitude disturbance can be straightforwardly obtained from the Base Attitude Disturbance Ellipsoid. In particular, for a planar space robot, we draw the useful conclusion that the impact direction unchanged base attitude must exist. Furthermore, the average axial length of the Base Attitude Disturbance Ellipsoid is used as a measurement to illustrate the average base attitude disturbance under impact impulses from different directions. With this measurement, the desired pre-impact configuration with minimum average base attitude disturbance can be easily determined.
TOPICS: Robots, Impulse (Physics), Jacobian matrices, Dynamic models, Computation
Yong Zhong, Jialei Song, Haoyong Yu and Ruxu Du
J. Mechanisms Robotics   doi: 10.1115/1.4040434
Recent state-of-art researches on robot fish focus on revealing different swimming mechanisms and developing control methods to imitate the kinematics of the real fish formulated by so-called Lighthill's theory. However, the reason why robot fish must follow this formula has not be fully studied. In this paper, we adopt a biomimetic untethered robot fish to study the kinematics of fish flapping. The robot fish consists of a wire-driven body and a soft compliant tail, which can perform undulatory motion using one motor. A dynamic model integrated with surrounding fluid is developed to predict the cruising speed, static thrust, dynamic thrust, and yaw stability of the robot fish. Three driving patterns of the motor are experimented to achieve three kinematic patterns of the robot fish, e.g. triangular pattern, sinusoidal pattern and an over-cambered sinusoidal pattern. Based on the experiment results, it is found that the sinusoidal pattern generated the largest average static thrust and steady cruising speed, while the triangular pattern achieved the best yaw stability. The over-cambered sinusoidal pattern was compromised in both metrics. Moreover, the kinematics study shown that the body curves of the robot fish were similar to the referenced body curves presented by the formula when using the sinusoidal pattern, especially the major thrust generation area. This research provides a guidance on the kinematic optimization and motor control of the undulatory robot fish.
TOPICS: Kinematics, Robots, Thrust, Motors, Stability, Yaw, Engines, Dynamic models, Fluids, Wire, Motor controls, Optimization, Biomimetics
Guanglei Wu, Shaoping Bai and Stéphane Caro
J. Mechanisms Robotics   doi: 10.1115/1.4040353
This paper presents a uniform method of evaluating both transmission quality and singularity applicable for a class of parallel Schoenflies-motion generators with four RRPaRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform. The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Four robots are compared based on the proposed indices as illustrative examples.
TOPICS: Generators, Robots, Jacobian matrices, Scalars, Pressure, Rotation
Design Innovation Paper  
Na Zhao, Yudong Luo, Hongbin Deng and Yantao Shen
J. Mechanisms Robotics   doi: 10.1115/1.4040355
This paper focuses on designing, kinematically and dynamically characterizing a novel deformable quad-rotor that is based on the scissor-like foldable mechanisms. Inspired by morphological adaptation of birds during flight, the quad-rotor allows that its volume can be varied to dynamically adapt complex environments and spaces. The advantages of such mechanism are twofold following the scenario, that is, the quad-rotor can stably fly with a big volume/size and can also switch to a smaller volume for a swift flight in response to the changes of the environments and spaces. It therefore is capable of efficiently avoiding obstacles, stably passing through narrow spaces, and resisting certain-extent wind effects. To generate the controllable deformation, the actuated angulated scissor elements in the structure play an important role. The scissor element design, its actuation mechanism and volume deformation of the new quad-rotor are presented in detail. Simulations and experiments are then conducted to validate the controlled deformation as well as to investigate the deformation elicited effects to the activated quad-rotor airframe and its aerodynamics. The results demonstrate the effectiveness of the proposed deformable quad-rotor, that is, it enables excellent volume deformation performance, good flight adaptation, as well as minimal aerodynamics influences during deforming.
TOPICS: Kinematics, Aerodynamics, Design, Rotors, Deformation, Space, Flight, Simulation, Switches, Wind, Engineering simulation
Chong Zhao, Hongwei Guo, Rong-qiang Liu, Zongquan Deng and Bing Li
J. Mechanisms Robotics   doi: 10.1115/1.4040356
Capturing noncooperative targets in space has great prospects for application. In this work, the unit of a large-scale reconfigurable space multifingered hand (LSRSMFH) for multitask requirements is studied. First, the lockable spherical (lS) joint, a new metamorphic joint that can function as Hooke (lS1) and spherical (lS2) joints and is driven by SMA material, is proposed. On the basis of the lS joint, this study presents a new metamorphic parallel mechanism (MPM), the 3RRlS MPM, which has four configurations, namely, 3RRlS1, 3RRlS2, 2RRlS1-RRlS2, and 2RRlS2-RRlS1. The degree of freedom (DOF), overconstraint and parasitic motions of the 3RRlS MPM are analyzed using screw theory, in which the DOF can be changed from 1 to 3. The 3RRlS1 configuration has a virtual constraint, and the 3RRlS2 configuration has linear parasitic motions along the X and Y axes. Finally, according to the spatial geometric conditions of the 3RRlS MPM, the parasitic motion equation is derived for verifying that the mechanism motion screws can represent mechanism parasitic motions.
TOPICS: Design, Parallel mechanisms, Screws, Equations of motion, Degrees of freedom
Xuesi Ma, Xinsheng Zhang and Jian S Dai
J. Mechanisms Robotics   doi: 10.1115/1.4040357
Classical mobility-one loop linkages usually have different assembled conditions, each of which has a configuration and a motion cycle. In normal circumstance, the linkage experienced a full cycle when the input joint completes a joint cycle. But some mechanisms have a motion cycle larger than 2pi because of the bifurcation motion. Bennett plano-spherical hybrid linkage is an over-constrained spatial 6R linkage with one degree of freedom. Its motion cycle can expand to , four times of a normal motion cycle. By mapping the two-dimensions of input-output relationship to a three-dimension configuration toroid, the motion cycle can be observed. Using intersection of the constraint curve with the bottom plane, top plane and equatorial plane, this linkage's motion can be divided into four parts, which are connected by the motion. During each part, the linkage will pass through configurations with a same joint input angular. Further, Myard plane-symmetry 5R linkage can have a motion cycle under a special condition. By mapping the input-output relationship onto the configuration toroid using the same method, the linkage's motion can be divided into two parts, during each of which the input joint angle accomplishes a full cycle, but the linkage itself only accomplishes half a cycle. In both linkages, the bifurcations connect different parts of motion curves and make them transform continuously and smoothly. This has been revealed in this paper though the motion branches transformation is not so apparent.
TOPICS: Linkages, Bifurcation, Mechanical admittance, Cycles, Dimensions, Degrees of freedom
Technical Brief  
Mengze Li, Zhaofan Yuan, Tadayoshi Aoyama and Yasuhisa Hasegawa
J. Mechanisms Robotics   doi: 10.1115/1.4040354
The research and development of powered exoskeletons carried out are expected for the walking support of paraplegic patients. At the current stage, exoskeletons do not allow patients to voluntarily control their gait or do not provide sensory feedback to make up for the loss of lower-body sensation. This paper proposes a wearable walking control interface to achieve voluntary gait control? and an electric stimulation method to inform the patients regarding their foot position for their voluntary gait control. In this study, a walking robot that simulates a paraplegic patient wearing an exoskeleton was used to investigate the performance of the proposed interface and stimulation method. We confirmed that using the interface, the subjects were able to control the robot gait for 3 meters distance; the accuracy of the electric stimulation feedback was confirmed to be close to the visual feedback achieved through human eyes. The experiment results indicate that the proposed interface and electrical stimulation feedback could be applied to a walking support system for complete paraplegic patients.
TOPICS: Robots, Feedback, Exoskeleton devices, Human eye, Industrial research

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