Academic literature on the topic 'Watt-II Mechanism'

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Journal articles on the topic "Watt-II Mechanism"

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Mirth, J. A., and T. R. Chase. "Circuit Analysis of Watt Chain Six-Bar Mechanisms." Journal of Mechanical Design 115, no. 2 (1993): 214–22. http://dx.doi.org/10.1115/1.2919180.

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A circuit is a distinct continuous range of motion of a mechanism. Changing circuits necessitates disassembling the mechanism. Thus, a designer must ensure a mechanism does not change circuits between two desired positions. A Watt chain is composed of two connected four-bar chains. A Watt chain may have one, two, three, or four circuits. The number of circuits and the extent of each circuit are shown to be determinable from the circuit attributes of the two component four-bars and by the limits of motion that these two four-bars place on each other. The circuit composition of all pin jointed Watt mechanisms is summarized in chart form. The chart enables detecting a change of circuit between any two trial positions of the same mechanism. The chart is suitable for both automated and manual analysis. Examples of circuit analysis of both Watt I and Watt II mechanisms are provided.
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Ye, Hang, Zhongke Niu, Dawei Han, et al. "Size optimization method of the Watt-II six-bar mechanism based on particle swarm optimization." Mechanical Sciences 16, no. 1 (2025): 237–44. https://doi.org/10.5194/ms-16-237-2025.

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Abstract. Aiming at the difficult problem of comprehensive scale design of the six-bar mechanism in engineering practice, kinematic and dynamic analysis and modeling of the Watt-II six-bar mechanism were carried out and combined with the particle swarm optimization (PSO) algorithm, the size optimization model of the Watt-II six-bar mechanism was established, and the size optimization of the Watt-II six-bar mechanism was completed. The results show that the optimized mechanism can improve the output capacity of the mechanism and reduce the force of the parts while ensuring the motion stability, which has certain practical significance in engineering.
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Kang, Yaw-Hong, Da-Chen Pang, and Dong-Han Zheng. "Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles." Machines 13, no. 7 (2025): 589. https://doi.org/10.3390/machines13070589.

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This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an inner wheel steering angle of 70 degrees. The mechanisms synthesized include the Ackermann steering mechanism and two variants (Type I and Type II) of the Watt-I six-bar steering mechanisms, also known as central-lever steering mechanisms. To ensure accurate steering and minimize tire wear during cornering, adherence to the Ackermann steering condition is enforced. The objective function combines the mean squared structural error at selected steering positions with a penalty term for violations of the Grashoff inequality constraint. Each optimization run involved 100 or 200 iterations, with numerical experiments repeated 100 times to ensure robustness. Kinematic simulations were conducted in ADAMS v2015 to visualize and validate the synthesized mechanisms. Performance was evaluated based on maximum structural error (steering accuracy) and mechanical advantage (transmission efficiency). The results indicate that the optimized Watt-I six-bar steering mechanisms outperform the Ackermann mechanism in terms of steering accuracy. Among the Watt-I variants, the Type II designs demonstrated superior performance and convergence precision compared to the Type I designs, as well as improved results compared to prior studies. Additionally, the optimal Type I-2 and Type II-2 mechanisms consist of two symmetric Grashof mechanisms, can be classified as non-Ackermann-like steering mechanisms. Both optimization methods proved easy to implement and showed reliable, efficient convergence. The DE-gr algorithm exhibited slightly superior overall performance, achieving optimal solutions in seven cases compared to four for the IPSO method.
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Jo, Min Seok, Jae Kyung Shim, Ho Sung Park, and Woon Ryong Kim. "Dimensional Synthesis of Watt II and Stephenson III Six-Bar Slider-Crank Function Generators for Nine Prescribed Positions." Applied Sciences 12, no. 20 (2022): 10503. http://dx.doi.org/10.3390/app122010503.

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This paper proposes an efficient exact dimensional synthesis method for finding all the link lengths of the Watt II and Stephenson III six-bar slider-crank function generators, satisfying nine prescribed precision points using the homotopy continuation method. The synthesis equations of each mechanism are initially constructed as a system of 56 quadratic polynomials whose Bézout number, which represents the maximum number of solutions, is 256 ≅ 7.21 × 1016. In order to reduce the size of the system, multi-homogeneous formulation is applied to transform the system into 12 equations in 12 unknowns, and the multi-homogeneous Bézout number of the system is 286,720. The Bertini solver, based on the homotopy continuation method, is used to solve the synthesis equations to obtain the dimensions of the two mechanisms. For the arbitrarily given nine precision points, the proposed method yields 37 and 31 defect-free solutions of Watt II and Stephenson III six-bar slider-crank mechanisms, respectively, and it is confirmed that they pass through the prescribed positions.
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Khalid, Nafees. "DIMENSIONAL SYNTHESIS OF WATT-II MECHANISM BASED ON TWENTY FOUR PRECISION POINTS PATH GENERATION." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 2 (2018): 319–27. https://doi.org/10.5281/zenodo.1173482.

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In this paper, a path generation problem has been solved by carrying out approximate dimensional synthesis of six-bar, single degree of freedom Watt-II mechanism. The mechanism consisting of all revolute pairs is capable to trace the prescribed trajectory which comprises of twenty four precision points. The dimensional synthesis is carried out using analytical complex number method wherein, the standard dyad/triad and loop closure equations are generated. The final lengths and orientations of various links of the mechanism are determined by solving these equations using a MATLAB code for twenty four coupler displacement positions. The dimensional synthesis of the mechanism is demonstrated and verified on a numerical example.
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KIPER, Gökhan. "FUNCTION GENERATION OF A WATT II TYPE PLANAR MECHANISM WITH PRISMATIC OUTPUT USING DECOMPOSITION AND CORRECTION METHOD." Machine Science Journal 3, no. 2 (2023): 20–27. http://dx.doi.org/10.61413/svmw4749.

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The method of decomposition is a useful method for function generation with multi-loop mechanisms. The recently introduced correction methods applied together with the method of decomposition allows the designer to cancel out the errors in the first loop of a two-loop mechanism with the errors in the second loop. In this study, the decomposition and correction method is applied for a Watt II type planar six-link mechanism with prismatic output. Five design parameters are defined for each loop resulting in ten design parameters in total. The design parameters are determined analytically. The generation error is decreased by adjusting free parameters such as the limits of the some joint angles and parameters due to the decomposition of the function to be generated, while considering several constraints such as link lengths ratios and ranges of the joint variables. The success of the method is illustrated with a numerical example.
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Simionescu, P. A., and M. R. Smith. "Initial Estimates in the Design of Rack-and-Pinion Steering Linkages." Journal of Mechanical Design 122, no. 2 (2000): 194–200. http://dx.doi.org/10.1115/1.533560.

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Based on recent results concerning the occurrence of function cognates in Watt II linkages, it is shown that only 3 geometric parameters are sufficient for defining the kinematic function of simplified planar rack-and-pinion steering linkages. The steering performances of the mechanisms are analytically expressed in terms of these parameters and, by employing an optimization-based synthesis method involving increasing the degree of freedom of the mechanism, the optimum domains are determined. The parameter sets corresponding to these minimum steering error domains are displayed in design charts. These charts aid the automotive engineer in the early stages of conceiving a new steering linkage by providing initial estimates of the basic geometry of the mechanism. They also provide information on two other characteristics of concern, i.e. the minimum pressure angle occurring in the joints and the rack stroke required for maximum turn of the wheels. [S1050-0472(00)00402-5]
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Lanese, Nicholas A., David H. Myszka, Anthony L. Bazler, and Andrew P. Murray. "Six-Bar Linkage Models of a Recumbent Tricycle Mechanism to Increase Power Throughput in FES Cycling." Robotics 11, no. 1 (2022): 26. http://dx.doi.org/10.3390/robotics11010026.

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This paper presents the kinematic and static analysis of two mechanisms to improve power throughput for persons with tetra- or paraplegia pedaling a performance tricycle via FES. FES, or functional electrical stimulation, activates muscles by passing small electrical currents through the muscle creating a contraction. The use of FES can build muscle in patients, relieve soreness, and promote cardiovascular health. Compared to an able-bodied rider, a cyclist stimulated via FES produces an order of magnitude less power creating some notable pedaling difficulties especially pertaining to inactive zones. An inactive zone occurs when the leg position is unable to produce enough power to propel the tricycle via muscle stimulation. An inactive zone is typically present when one leg is fully bent and the other leg is fully extended. Altering the motion of a cyclist’s legs relative to the crank position can potentially reduce inactive zones and increase power throughput. Some recently marketed bicycles showcase pedal mechanisms utilizing alternate leg motions. This work considers performance tricycle designs based on the Stephenson III and Watt II six-bar mechanisms where the legs define two of the system’s links. The architecture based on the Stephenson III is referred to throughout as the CDT due to the legs’ push acting to coupler-drive the four-bar component of the system. The architecture based on the Watt II is referred to throughout as the CRT due to the legs’ push acting to drive the rocker link of the four-bar component of the system. The unmodified or traditional recumbent tricycle (TRT) provides a benchmarks by which the designs proposed herein may be evaluated. Using knee and hip torques and angular velocities consistent with a previous study, this numerical study using a quasi-static power model of the CRT suggests a roughly 50% increase and the CDT suggests roughly a doubling in average crank power, respectively, for a typical FES cyclist.
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Bahri, Samsul. "Torque and Power Consumption of Paddlewheel Aerator With Movable Blade." Malikussaleh Journal of Mechanical Science and Technology 3, no. 2 (2015): 6. http://dx.doi.org/10.29103/mjmst.v3i2.10897.

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The development of movable blade is based on fact that power is required only when blade of paddle wheel aerator entering water and in contrary action of aeration effect only when the blade is about leaving the water. This study was carrier out to design and simulate paddle wheel aerator with movable blade which will open when entering water and close when leaving water. Wheel closed at quadrant I to IV (entering water surface) and was about to open at quadrant III to II (leaving water surface). The blade was designed referring to commonly used Taiwan wheel type. The component of mobable blade mechanism consisted of cam and shaft, velg, velg cap, blade holder, follower, spring and bearing. Follower was able rotate with angle of rotation was 125°, rotational displacement was 50 mm, maximum velocity was 0.55 m/s and acceleration was 6.09 m/s2. Testing without a load at 115 rpm shows the torque that occured 43.05 N and the electric power used 511.72 Watt. The gain is smaller than the increase of torque and power needed for movable blade paddlewheel aerator mechanism
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Gibson, C. G., and D. Marsh. "On the linkage varieties of watt 6-bar mechanisms—II. The possible reductions." Mechanism and Machine Theory 24, no. 2 (1989): 115–21. http://dx.doi.org/10.1016/0094-114x(89)90018-9.

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Dissertations / Theses on the topic "Watt-II Mechanism"

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JHANG, BO, and 張栢. "Optimal Dimensional Synthesis and Kinetostatic Analysis of Watt-II Six-bar Walking Mechanism." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/gx7g84.

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碩士<br>國立高雄應用科技大學<br>機械工程系<br>106<br>In this study, five evolutionary algorithms-a genetic algorithm (GA), particle swarm optimization (PSO), hybrid particle swarm optimization (HPSO), differential evolution (DE), and self-adaptive differential evolution (SaDE)-were used to optimize dimensional synthesis for the path generation mechanisms of four-bar linkages and Watt-II six-bar linkages. The dimensional synthesis was optimized by minimizing the objective function, which was defined as the sum of squares of the distance error between design points and trajectories of coupler-point of generated mechanisms. Through dimensional synthesis performed on eight different coupler-point trajectories for the path generation of four-bar linkages, the comparisons were made for the rate of convergence of all optimization methods, as well as the errors between coupler-point trajectories of synthesized mechanisms. The results indicated that the SaDE algorithm outperformed the other four evolutionary algorithms, as well as the algorithms adopted in previous studies. Accordingly, the SaDE algorithm may be applicable to the dimensional synthesis problem of multi-loop path generation mechanisms. Because Watt-II six-bar linkages have applications in prosthetics and robot feet, this study employed the vector loop method to derive the kinematic relation of the parameters of the mechanism and performed a kinetostatic analysis to yield a dynamic matrix for solving all joint forces. Subsequently, 11 points on the ideal human walking trajectory were used as design points; the five aforementioned evolutionary algorithms were adopted under kinematic and geometric restrictions to perform optimal dimensional synthesis of Watt-II six-bar leg mechanisms. The results of this synthesis suggested that the SaDE algorithm outperformed the other algorithms in determining the optimal dimensions of the mechanisms. Afterwards, a MATLAB program was written to analyze the kinematic properties and all joint forces of the SaDE-derived optimal Watt-II six-bar leg mechanism. Furthermore, ADAMS was used to perform coupler-point trajectories and dynamic analyses, thereby validating the results obtained through the MATLAB program. Finally, the walking mechanism of a four-leg robot was constructed by assembling four identical Watt-II six-bar linkages symmetrically between the left and right sides but in reverse order between the front and back; ADAMS was then used to simulate the trajectory of the robot’s walking motion and perform a dynamic analysis. In summary, this study used a SaDE algorithm for the optimal dimensional synthesis of Watt-II six-bar linkages and confirmed that the SaDE algorithm had a higher rate of convergence and more satisfactory results than the other evolutionary algorithms. The findings are expected to improve the optimization and design of other complex multi-loop linkages.
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Kao, Min-Cheng, and 高敏城. "The synthesis of Watt II toggle mechanisms." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/92293111918184631205.

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Books on the topic "Watt-II Mechanism"

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McNaughton, James. Beckett in History. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822547.003.0004.

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Drawing from the archive of Beckett’s letters, vocabulary notebooks, and German Diaries, this chapter elaborates Beckett’s encounters with propaganda in Nazi Germany, and demonstrates how Watt formally performs the interpretative problems propaganda presents. The word games in the book make sense when read in light of Adorno’s claim that fascism first found a refuge in mystified language. The novel presents strategies by which the character Watt refuses to resist the mystification of power and the ideological seduction of Mr. Knott’s house. More, the book evokes and then dismisses recent and violent history by bringing to mind remnants of historical images from World War II. The formal games and near-autonomy of the entire work, combined with its Irish setting, threaten to override or erase such vestiges of history, as if literary form demonstrates the mechanics of propaganda itself, recontextualizing and diminishing the menacing image that it evokes.
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Book chapters on the topic "Watt-II Mechanism"

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Schwarzfischer, F., M. Hüsing, and B. Corves. "The Dynamic Synthesis of an Energy-Efficient Watt-II-Mechanism." In Multibody Mechatronic Systems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67567-1_20.

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Kiper, Gökhan. "Motion Synthesis of a Planar Watt II Type Six-Bar Mechanism with Two End-Effectors." In Mechanisms, Transmissions and Applications. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17067-1_10.

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Conference papers on the topic "Watt-II Mechanism"

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Pan, C. A., D. Kohli, and A. K. Dhingra. "Double Points and Unstable Configurations of Watt-I and Watt-II Mechanisms." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/mech-14201.

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Abstract Double points are conjugate configurations in mechanisms, with multiple closed-loops, when both input and output links are fixed in the same position and some passive joints can be located in two different configurations. Unstable configurations, on other hand, are positions where a mechanism loses controllability and gains at least one unwanted DOF instantaneously. The analytical condition for the occurrence of double point is the same as the occurrence of an unstable configuration, i.e., two roots of input-output displacement polynomial are equal. This paper addresses the determination of double points and unstable configurations of six-link Watt-I and Watt-II mechanisms. The double points are determined by using the loop-closure equations for two branches and successively eliminating intermediate joint variables using closed-form techniques. Further, extraneous roots from algebraic manipulations are eliminated using a new technique of two-branch equation substitution. The unstable configuration polynomial is derived by (i) successively eliminating intermediate variables from loop-closure equations to obtain the input-output displacement polynomial, (ii) equating the polynomial discriminant to zero to obtain a polynomial which contains both unstable configurations and double points, and (iii) eliminating extraneous roots from algebraic manipulations and double points from this composite polynomial to determine the unstable configurations. The computational procedure is illustrated through numerical examples.
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Mirth, John A. "The Application of Geometric Constraint Programming to the Design of Motion Generating Six-Bar Linkages." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70176.

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This paper looks at the application of Geometric Constraint Programming (GCP) to the synthesis of six-bar planar linkages. GCP is a synthesis method that relies on the built-in geometric capabilities of commercial solid-modeling programs to produce linkage designs while operating in the “sketch” mode for these programs. GCP provides the user with the opportunity to create mechanisms in their entirety at multiple design positions. The complexity of analyzing potential defects (such as circuit or branch defects) within a six-bar mechanism poses significant challenges to the user who might try to design such a mechanism in a single step. The methods presented in this paper apply GCP in a stepwise manner to create six-bar linkages that are less likely to suffer from defects than if they were created in a single step. Stepwise approaches are presented for six-bar mechanisms designed to solve a problem involving rigid-body guidance (motion generation). The linkages considered include the Stephenson I, II, and III chains, as well as the Watt I six-bar. The Watt II six-bar is not included since this mechanism’s application to rigid-body guidance can be handled by GCP methods previously developed for four-bar linkages.
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Berge, Nathan, and Matthew I. Campbell. "Optimal Linkage Shapes of Planar Mechanisms Using Topology Optimization." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65186.

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Through the methods outlined in this paper, a procedure involving two cooperating optimization algorithms is developed to create balanced, structurally optimal planar mechanisms. Two systems are analyzed to demonstrate the approach. In the first example, a walking mechanism is analyzed under quasi-static loading, and topology optimization is performed to create stiff, lightweight linkages. In the second example, a quick-return Watt-II six-bar mechanism, counterweights are added to balance the mechanism using a numerical optimization technique. The inertial forces are calculated by simulation, and optimal linkage shapes are generated to support them using topology optimization.
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Herrera-Perez, Martin S., Kristen Morse, Md Minal Nahin, and James D. Van de Ven. "Flow Ripple Minimization in a Triplex Pump Through the Implementation of Various Linkage Mechanisms." In ASME/BATH 2023 Symposium on Fluid Power and Motion Control. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/fpmc2023-111788.

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Abstract A significant amount of research has been conducted to reduce the outlet flow ripple in pumps. The approach usually focuses on techniques to improve valve timing, but few attempts have been made to achieve this improvement from the piston trajectory itself. This paper investigates how the flow ripple in a triplex pump is influenced by the implementation of different linkage mechanisms that allow direct tuning of the piston trajectory. The model of a baseline pump with a displacement of 10 cc/rev and operating pressures that range from 5 to 50 MPa is built to account for the kinematics and pressure dynamics of three linkage configurations: (1) inline crank-slider, (2) offset crank-slider, (3) Watt-II crank-slider. The kinematics of the linkage configurations (2) and (3) are optimized to minimize output flow ripple. Flow ripple reductions of 10% and 25% are found for the offset crank-slider and Watt-II crank-slider respectively, compared with the inline crank-slider. Tradeoffs between kinematic and dynamic flow ripple are observed as the pump model is evaluated at various operating pressures. An optimum Watt-II linkage mechanism with a kinematic and dynamic flow ripple of 10.6% at 5 MPa is found and described in this paper along with its performance across a wide range of operating pressures.
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Marquez, Eleazar, Robert A. Freeman, and Horacio Vasquez. "Development and Testing of an Actively Adjustable Stiffness Mechanism." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39033.

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This study presents the comparison of the theoretical and experimental results of the performance of an adjustable stiffness mechanism. In particular, the use of redundant actuation is emphasized in the design of a one degree-of-freedom Watt II mechanism capable of independently controlling the effective stiffness without a change in equilibrium position. This approach is in contrast to spring mechanism designs unable to actively control the spring rate independent of deflection, and with potential applications in various types of suspension and assembly systems. Results indicate that two direct drive brush-type direct current motors are required to drive the redundantly actuated mechanism and create a system that behaves as an adjustable stiffness spring.
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Yi, Lu, and Tatu Leinonen. "Computer Simulation of Path and Motion Generation With Six-Bar Linkage." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dac-48831.

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The basic tool of path or motion generation synthesis for more than four prescribed positions is analytical calculation, but its process is quite complicated and far from straightforward. A novel computer simulation mechanism of six-bar linkage for path or motion generation synthesis is presented in this paper. In the case of five-precision points, using the geometric constraint and dimension-driving techniques, a primary simulation mechanism of four-bar linkage is created. Based on the different tasks of path and motion generation for kinematic dimensional synthesis, the simulation mechanisms of path and motion generation with Stephenson I, II and Watt six-bar linkages are developed from the primary simulation mechanism. The results of kinematic synthesis for five prescribed positions prove that the mechanism simulation approach is not only fairly quick and straightforward, but is also advantageous from the viewpoint of accuracy and repeatability.
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Li, Lin, David H. Myszka, Andrew P. Murray, and Charles W. Wampler. "Using the Singularity Trace to Understand Linkage Motion Characteristics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13244.

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This paper provides examples of a method used to analyze the motion characteristics of single-degree-of-freedom, closed-loop linkages under study a designated input angle and one or two design parameters. The method involves the construction of a singularity trace, which is a plot that reveals changes in the number of geometric inversions, singularities, and changes in the number of branches as a design parameter is varied. This paper applies the method to Watt II, Stephenson III and double butterfly linkages. For the latter two linkages, instances where the input angle is able to rotate more than one revolution between singularities have been identified. This characteristic demonstrates a net-zero, singularity free, activation sequence that places the mechanism into a different geometric inversion. Additional observations from the examples are given. Instances are shown where the singularity trace for the Watt II linkage includes multiple coincident projections of the singularity curve. Cases are shown where subtle changes to two design parameters of a Stephenson III linkage drastically alters the motion. Additionally, isolated critical points are found to exist for the double butterfly, where the linkage becomes a structure and looses the freedom to move.
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Del Rosario, Aaron Jules R., Aristotle T. Ubando, and Alvin B. Culaba. "Kinematic Synthesis and Analysis of a Watt II Six-Bar Linkage for the Design and Validation of an Open Loop Solar Tracking Mechanism." In 2019 IEEE 11th International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management ( HNICEM ). IEEE, 2019. http://dx.doi.org/10.1109/hnicem48295.2019.9072698.

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Larochelle, Pierre, Jugesh Sundram, and Ronald A. Zimmerman. "Synthesis of Watt II Mechanisms for Four Simultaneous Positions." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46045.

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This article presents the kinematic synthesis of Watt II six-bar mechanisms for simultaneously guiding two bodies through four prescribed positions. The two bodies to be moved are connected by a revolute joint and the motion generation task is defined by the four desired positions of one body and the relative angle of the second body with respect to the first body. The methodology uses an algebraic geometry formulation of the exact synthesis of planar RR dyads for four prescribed positions from classical Burmester theory. The result is a dimensional synthesis technique for designing Watt II mechanisms for four simultaneous positions. A case study illustrating the application of the synthesis algorithm is included.
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Dhingra, Anoop K., Jyun-Cheng Cheng, and Dilip Kohli. "Complete Solutions to Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With M-Homogenization." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0308.

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Abstract This paper presents complete solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining compatibility equations in addition to the synthesis equations, the number of homotopy paths to be tracked can be drastically reduced. For Watt’s six-link function generators with 6 thru 11 precision positions, the number of homotopy paths to be tracked in obtaining all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. For 6, 7 and 8 point slider-crank path generation problems, the number of paths to be tracked are 320, 3840 and 17,920, respectively, whereas for four-link path generators with 6 thru 8 positions these numbers range from 640 to 71,680. It is also shown that for body guidance problems of slider-crank and four-link mechanisms, the number of homotopy paths to be tracked is exactly same as the maximum number of possible solutions given by the Burmester-Ball theories. Numerical results of synthesis of slider-crank path generators for 8 precision positions and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.
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