Mechanism Design Visual and Programmable Approaches Kevin Russell Qiong Shen Raj S Sodhi Tai ngay!!! Ban co the xoa dong chu nay!!! Mechanism Design Visual and Programmable Approaches Mechanism Design Visual and Programmable Approaches Kevin Russell Qiong Shen Raj S Sodhi Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business MATLAB® is a trademark of The MathWorks, Inc and is used with permission The MathWorks does not warrant the accuracy of the text or exercises in this book This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20131021 International Standard Book Number-13: 978-1-4665-7018-4 (eBook - PDF) This book contains information obtained from 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from this work, please access www.copyright.com (http://www copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-7508400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To Willie J Russell and in memory of Ella Russell Kevin Russell To my parents, Youlin Shen and Mantian Wang, without whom none of my success would be possible Qiong Shen To my parents, Rachpal S and Pritpal K Sodhi Raj S Sodhi Contents Preface .xi Authors xv Chapter Introduction to Kinematics 1.1 Kinematics 1.2 Kinematic Chains and Mechanisms 1.3 Mobility 1.4 Summary References Additional Reading .6 Chapter Mobility of Mechanisms 2.1 Planar Mechanism Types 2.2 Links, Joints, and Mechanism Mobility 2.3 Number Synthesis 12 2.4 Grashof’s Criteria and Transmission Angle 14 2.5 Summary 17 Problems 17 References 20 Chapter Kinematics of Planar Mechanisms 21 3.1 3.2 Kinematic Analysis of Planar Mechanisms 21 Four-Bar Mechanism Analysis 21 3.2.1 Four-Bar Displacement Equation 21 3.2.2 Four-Bar Velocity Equation 22 3.2.3 Four-Bar Acceleration Equation 23 3.3 Slider-Crank Mechanism Analysis 25 3.3.1 Slider-Crank Displacement Equation 25 3.3.2 Slider-Crank Velocity Equation 26 3.3.3 Slider-Crank Acceleration Equation 27 3.4 Multiloop Mechanism Analysis 29 3.5 Kinematics of Mechanism Locations of Interest 31 3.6 Solution Method for Vector Loop Kinematic Equations 33 3.7 Planar Kinematic Modeling in MATLAB® and SimMechanics® .34 3.8 Summary 38 Problems 39 References 44 Additional Reading 44 vii viii Contents Chapter Kinematic Synthesis and Planar Four-Bar Motion Generation 45 4.1 4.2 4.3 Introduction to Kinematic Synthesis 45 Branch and Order Defects 47 Motion Generation: Three, Four, and Five Precision Positions 49 4.4 Branch and Order Defect Elimination: Three, Four, and Five Precision Positions 62 4.5 Summary 66 Problems 67 References 75 Chapter Planar Four-Bar and Multiloop Path and Motion Generation 77 5.1 5.2 5.3 5.4 5.5 Path Generation versus Motion Generation 77 Coupler Curves and Dwell Motion 78 Approximate Four-Bar Path and Motion Generation .80 Alternate Four-Bar Kinematic Equations 86 Alternate Approximate Four-Bar Motion and Path Generation Equations 88 5.6 Constructing Cognates 92 5.7 Analytical and Approximate Multiloop Path and Motion Generation 100 5.8 Summary 104 Problems 105 References 116 Chapter Planar Four-Bar Function Generation 117 6.1 6.2 Introduction to Function Generation 117 Function Generation: Three, Four, and Five Precision Points 119 6.3 Approximate Function Generation 122 6.4 Velocity and Acceleration Constraints for Function Generation 125 6.5 Function Generation with Finite and Multiply Separated Positions 127 6.6 Approximate Function Generation with Finite and Multiply Separated Positions 129 6.7 Summary 130 Problems 131 References 136 Additional Reading 136 Chapter Spatial Mechanism Kinematics and Synthesis 137 7.1 7.2 Introduction to Spatial Four-Bar Mechanisms 137 RRSS and 4R Spherical Mechanism Analysis 137 ix Contents 7.3 7.4 RSSR and 4R Spherical Mechanism Analysis 141 Approximate RRSS and 4R Spherical Motion and Path Generation 143 7.5 Approximate RSSR and 4R Spherical Function Generation 160 7.6 RSSR–SS Mechanism Analysis 166 7.7 R–S Dyad and Approximate RSSR–SS Motion Generation 170 7.8 Spatial Kinematic Modeling in MATLAB® and SimMechanics® 176 7.9 Summary 177 Problems 178 References 186 Chapter Adjustable Planar and Spherical Four-Bar Mechanism Synthesis 187 8.1 8.2 Introduction to Adjustable Mechanism Synthesis 187 Approximate Adjustable Planar Four-Bar Motion Generation 190 8.3 Approximate Adjustable Planar Four-Bar Motion and Path Generation: Alternate Equations 194 8.4 Approximate Adjustable Planar Four-Bar Function Generation 199 8.5 Approximate Adjustable 4R Spherical Motion Generation 202 8.6 Approximate Adjustable 4R Spherical Motion and Path Generation: Alternate Equations 207 8.7 Summary 211 Problems 212 References 223 Appendix A: S olution Algorithm for Analytical Four-Position Synthesis and MATLAB® File User Instructions 225 Appendix B: Solution Algorithm for Analytical Five-Position Synthesis and MATLAB® File User Instructions 231 Appendix C: User Instructions for Chapter MATLAB® Files 239 Appendix D: User Instructions for Chapter MATLAB® Files 255 Appendix E: User Instructions for Chapter MATLAB® Files 263 Appendix F: User Instructions for Chapter MATLAB® Files 299 Appendix G: User Instructions for MATLAB® and SimMechanics® Files 327 Appendix G: User Instructions for MATLAB® and SimMechanics® Files 331 TABLE G.4 Output Files from Appendix G.2 MATLAB® and SimMechanics® Filesa Filename Contents (See Figure G.4 for Mechanism Reference) b1_disp.csv b1_vel.csv b1_acc.csv a1_ang_disp.csv a1_ang_vel.csv a1_ang_acc.csv X, Y, and Z coordinates of slider point b1 Velocity X, Y, and Z components of slider point b1 Acceleration X, Y, and Z components of slider point b1 Angular displacement (in degrees) about moving pivot a1 Angular velocity (in rad/s) about moving pivot a1 Angular acceleration (in rad/s2) about moving pivot a1 a The mechanism output in these files is written for each increment of the crank rotation range defined in Slider_Crank_Simulate.m a1 iY V1 W1 X G1 U1 b1 FIGURE G.4 Slider-Crank mechanism running Slider_Crank_Simulate.m, a graphical user interface appears where the slider-crank mechanism motion is simulated over the defined crank rotation range To replay the simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) When using the noted minimum values for step_ang in Planar_4Bar_Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) G.3 STEPHENSON III MECHANISM The Appendix G.3 folder (which is available for download at www.crcpress.com) includes three MATLAB and SimMechanics files for the kinematic analysis and simulation of Stephenson III mechanisms These three files are described in Table G.5 To conduct a kinematic analysis, the user specifies the mechanism link dimensions and the 332 Appendix G: User Instructions for MATLAB® and SimMechanics® Files TABLE G.5 Appendix G.3 MATLAB® and SimMechanics® Files Filename Stephenson_III_Simulate.m Stephenson_III_Model.mdl Post_Simulation_Task.m Use of File To specify mechanism link dimensions and crank link controls To calculate mechanism output and simulate mechanism motion To write mechanism output (compatible with Microsoft Excel) crank motion parameters in the file Stephenson_III_Simulate.m Values are specified for link variables W1, V1, G1, U1, L1, V1*, U1*, and G1* Values are also specified for the initial crank angle (start_ang), the crank rotation increment (step_ang), and the final crank angle (stop_ang) Lastly, values for the crank angular velocity (angular_vel) and angular acceleration (angular_acc) are specified also Figure G.5 illustrates the user input sections of the file Stephenson_III_Simulate.m with sample values given in bold.*,†,‡ % % Here, values for the Stephenson III mechanism variables W1, % V1, G1, U1, L1, V1s, U1s and G1s are assigned W1 = 1.0exp(i*90*pi/180); V1 = 1.5*exp(i*4.2451*pi/180); G1 = 1.5*exp(-i*15*pi/180); U1 = 1.5*exp(i*88.2046*pi/180); L1 = 1.5*exp(i*60*pi/180); V1s = 3.5*exp(–i*24.0302*pi/180); U1s = 3.5*exp(i*67.2115*pi/180); G1s = 2.2923*exp(–i*59.8309*pi/180); % % % Here, values for the start, step and stop displacement % angles for the crank link are assigned start_ang = 0; step_ang = 1; stop_ang = 360; % % % Here, values for crank link angular velocity and angular % acceleration are assigned angular_vel = 1.1 * ones(N,1); angular_acc = 1.2 * ones(N,1); % - FIGURE G.5 Sections of Stephenson_III_Simulate.m with sample values given in bold * If crank angular velocity and/or angular acceleration values are not required for the kinematic analysis, the user can specify zero for these variables † The units for crank rotation, angular velocity, and acceleration are degree, rad/s, and rad/s2 , respectively ‡ Only positive or negative integer values should be specified for start_ang and stop_ang The authors recommend minimum values of ±1, ±0.1, ±0.01, or ±0.001 for step_ang Appendix G: User Instructions for MATLAB® and SimMechanics® Files 333 After specifying the mechanism dimensions and driving link parameters in the file Stephenson_III_Simulate.m, the next step is to run this file To run the file, the user can use the “F5” button or click the Run Stephenson_III_Simulate.m button in the toolbar.* When running this file, 15 files are written in a folder named Results (in a format compatible with Microsoft Excel format) that includes calculated mechanism output at each crank link rotation increment The 15 files are described in Table G.6 Also, when running Stephenson_III_Simulate.m, a graphical user interface appears where Stephenson III mechanism motion is simulated in motion over the defined crank rotation range To replay the simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) When using the noted minimum values for step_ang in Planar_4Bar_Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) TABLE G.6 Output Files from Appendix G.3 MATLAB® and SimMechanics® Filesa Filename Contents (See Figure G.6 for Mechanism Reference) p1_disp.csv p1_vel.csv p1_acc.csv b0_ang_disp.csv b0_ang_vel.csv b0_ang_acc.csv a1_ang_disp.csv a1_ang_vel.csv a1_ang_acc.csv X, Y, and Z coordinates of coupler point p1 Velocity X, Y, and Z components of coupler point p1 Acceleration X, Y, and Z components of coupler point p1 Angular displacement (in degrees) about fixed pivot b0 Angular velocity (in rad/s) about fixed pivot b0 Angular acceleration (in rad/s2) about fixed pivot b0 Angular displacement (in degrees) about moving pivot a1 Angular velocity (in rad/s) about moving pivot a1 Angular acceleration (in rad/s2) about moving pivot a1 b0s_ang_disp.csv Angular displacement (in degrees) about fixed pivot b b0s_ang_vel.csv Angular velocity (in rad/s) about fixed pivot b b0s_ang_acc.csv b1s_ang_disp.csv * * * Angular acceleration (in rad/s2) about fixed pivot b * Angular displacement (in degrees) about moving pivot b1 * b1 b1s_ang_vel.csv Angular velocity (in rad/s) about moving pivot b1s_ang_acc.csv Angular acceleration (in rad/s2) about moving pivot b1 a * The mechanism output in these files is written for each increment of the crank rotation range defined in Stephenson_III_Simulate.m * This button is a green triangle (over a white square) and the text Run Stephenson_III_Simulate.m appears when the cursor is over it 334 Appendix G: User Instructions for MATLAB® and SimMechanics® Files p1 V1* L1 a1 V1 b*1 iY W1 X U1 G1 b0 U1* G1* b0* FIGURE G.6 Stephenson III mechanism G.4 RRSS MECHANISM The Appendix G.4 folder (which is available for download at www.crcpress.com) includes three MATLAB and SimMechanics files for the kinematic analysis and simulation of RRSS mechanisms These three files are described in Table G.7 To conduct a kinematic analysis, the user specifies the mechanism link dimensions and the crank motion parameters in the file RRSS_Simulate.m Values are specified for link variables a0, ua0, a1, ua1, b0, b1, p1, q1, and r1 Additionally, values are specified for the initial crank angle (start_ang), the crank rotation increment (step_ang), and the final crank angle (stop_ang) Figure G.7 illustrates the user input sections of the file RRSS_Simulate.m with sample values given in bold.* TABLE G.7 Appendix G.4 MATLAB® and SimMechanics® Files Filename RRSS_Simulate.m RRSS_Model.mdl Post_Simulation_Task.m Use of File To specify mechanism link dimensions and crank link controls To calculate mechanism output and simulate mechanism motion To write mechanism output (compatible with Microsoft Excel) * Only positive or negative integer values should be specified for start_ang and stop_ang The authors recommend minimum values of ±1, ±0.1, ±0.01, or ±0.001 for step_ang Appendix G: User Instructions for MATLAB® and SimMechanics® Files 335 % % Here, values for the RRSS mechanism variables a0, ua0, a1, ua1, % b0, b1 and coupler points P1, Q1 and R1 are assigned a0 = [0, 0, 0]; ua0 = [0, 0, 1]; a1 = [–0.5, 0, 0]; ua1 = [0, 0, 1]; b0 = [1.5, 0, 0]; b1 = [1.5, 1.5, 0]; P1 = [0.1, 0.2, 0.9747]; Q1 = [0.2, 0.3, 1]; R1 = [–0.3, –1, 0]; % % % Here, values for the start, step and stop displacement angles % for the crank link are assigned start_ang step_ang stop_ang = 0; = 30; = 360; % - FIGURE G.7 Sections of RRSS_Simulate.m with sample values given in bold TABLE G.8 Output Files from Appendix G.4 MATLAB® and SimMechanics® Filesa Filename p1_disp.csv q1_disp.csv r1_disp.csv a Contents (See Figure G.8 for Mechanism Reference) X, Y, and Z coordinates of coupler point p1 X, Y, and Z coordinates of coupler point q1 X, Y, and Z coordinates of coupler point r1 The mechanism output in these files is written for each increment of the crank rotation range defined in rows 26 through 28 in RRSS_Simulate.m After specifying the mechanism dimensions and driving link parameters in the file RRSS_Simulate.m, the next step is to run this file To run the file, the user can use the “F5” button or the Run RRSS_Simulate.m button in the toolbar.* When running this file, three files are written in a folder named Results (in a format compatible with Microsoft Excel) that includes calculated mechanism output at each crank link rotation increment The three files are described in Table G.8 Also, when running RRSS_Simulate.m, a graphical user interface appears where RRSS mechanism * This button is a green triangle (over a white square) and the text Run RRSS_Simulate.m appears when the cursor is over it 336 Appendix G: User Instructions for MATLAB® and SimMechanics® Files Rigid-body variables (e.g., p1, q1, r1) b1 a1 ua1 Y X ua0 a0 Z b0 FIGURE G.8 RRSS mechanism motion is simulated in motion over the defined crank rotation range.* To replay this simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) When using values ±0.1, ±0.01, or ±0.001 for step_ang in RRSS_Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) G.5 RSSR MECHANISM The Appendix G.5 folder (which is available for download at www.crcpress.com) includes three MATLAB and SimMechanics files for the kinematic analysis and simulation of RSSR mechanisms These three files are described in Table G.9 TABLE G.9 Appendix G.5 MATLAB® and SimMechanics® Files Filename RSSR_Simulate.m RSSR_Model.mdl Post_Simulation_Task.m Use of File To specify mechanism link dimensions and crank link controls To calculate mechanism output and simulate mechanism motion To write mechanism output (compatible with Microsoft Excel) * The passive DOF in the S-S link must be eliminated to produce a working RRSS simulation in SimMechanics To achieve this, a massless S-S link (which is not visible in a simulation) is used As a result, the S-S link does not appear in the RRSS simulation Appendix G: User Instructions for MATLAB® and SimMechanics® Files 337 % % Here, values for the RSSR mechanism variables a0, ua0, a1, b0, % ub0 and b1 are assigned a0 = [0, 0, 0]; ua0 = [0, 0, 1]; a1 = [0, 0.5, 0]; b0 = [1, 0, 1]; ub0 = [0, 0, 1]; b1 = [1, 1.5, 1]; % % % Here, values for the start, step and stop displacement angles % for the crank link are assigned start_ang = 0; step_ang = 1; stop_ang = 360; % - FIGURE G.9 Sections of RSSR_Simulate.m with sample values given in bold To conduct a kinematic analysis, the user specifies the mechanism link dimensions and the crank motion parameters in the file RSSR_Simulate.m Values are specified for link variables a0, ua0, a1, b0, ub0, and b1 Additionally, values are specified for the initial crank angle (start_ang), the crank rotation increment (step_ang), and the final crank angle (stop_ang) Figure G.9 illustrates the user input sections of the file RSSR_Simulate.m with sample values given in bold.* After specifying the mechanism dimensions and driving link parameters in the file RSSR_Simulate.m, the next step is to run this file To run the file, the user can use the “F5” button or the Run RSSR_Simulate.m button in the toolbar.† When running this file, a single file is written in a folder named Results (in a format compatible with Microsoft Excel) that includes calculated mechanism output at each crank link rotation increment The file is described in Table G.10 Also, when running RSSR_ Simulate.m, a graphical user interface appears where RSSR mechanism motion is simulated in motion over the defined crank rotation range.‡ To replay this simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) When using values ±0.1, ±0.01, or ±0.001 for step_ang in the file RSSR_ Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with * Only positive or negative integer values should be specified for start_ang and stop_ang The authors recommend minimum values of ±1, ±0.1, ±0.01, or ±0.001 for step_ang † This button is a green triangle (over a white square) and the text Run RSSR_Simulate.m appears when the cursor is over it ‡ The passive DOF in the S-S link must be eliminated to produce a working RSSR simulation in SimMechanics® To achieve this, a massless S-S link (which is not visible in a simulation) is used As a result, the S-S link does not appear in the RSSR simulation 338 Appendix G: User Instructions for MATLAB® and SimMechanics® Files TABLE G.10 Output File from Appendix G.5 MATLAB® and SimMechanics® Filesa Contents (See Figure G.10 for Mechanism Reference) Filename Angular displacement (in degrees) about joint axis ub0 ub0_ang_disp.csv a The mechanism output in these files is written for each increment of the crank rotation range defined in RSSR_Simulate.m b1 a1 Y X Z ua0 a0 ub0 b0 FIGURE G.10 RSSR mechanism a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) G.6 4R SPHERICAL MECHANISM Appendix G.6 folder (which is available for download at www.crcpress.com) includes three MATLAB and SimMechanics files for the kinematic analysis and simulation of 4R Spherical mechanisms These three files are described in Table G.11 To conduct a kinematic analysis, the user specifies the mechanism link dimensions and the crank motion parameters in the file RRRR_Spherical_Simulate.m Values are specified for link variables a0, a1, b0, b1, p1, q1, and r1 Additionally, values are specified for the initial crank angle (start_ang), the crank rotation increment (step_ang), and the final crank angle (stop_ang) Figure G.11 illustrates the user input sections of the file RRRR_Spherical_Simulate.m with sample values given in bold.* * Only positive or negative integer values should be specified for start_ang and stop_ang The authors recommend minimum values of ±1, ±0.1, ±0.01, or ±0.001 for step_ang Appendix G: User Instructions for MATLAB® and SimMechanics® Files 339 TABLE G.11 Appendix G.11 MATLAB® and SimMechanics® Files Filename RRRR_Spherical_Simulate.m RRRR_Spherical_Model.mdl Post_Simulation_Task.m Use of File To specify mechanism link dimensions and crank link controls To calculate mechanism output and simulate mechanism motion To write mechanism output (compatible with Microsoft Excel) % % Here, values for the 4R Spherical mechanism variables a0, a1, % b0 and b1 and coupler points P1, Q1 and R1 are assigned a0 a1 b0 b1 P1 Q1 R1 = = = = = = = [0, 0, 1]; [–0.7071, 0, 0.7071]; [1, 0, 0]; [0, 1, 0]; [0.1, 0.2, 0.9747]; [0.2, 0.3, 1]; [–0.3, –1, 0]; % % % Here, values for the start, step and stop displacement angles % for the crank link are assigned start_ang = 0; step_ang = 30; stop_ang = 360; % - FIGURE G.11 Sections of RRRR_Spherical_Simulate.m with sample values given in bold After specifying the mechanism dimensions and driving link parameters in the file RRRR_Spherical_Simulate.m, the next step is to run this file To run the file, the user can use the “F5” button or the Run RRRR_Spherical_Simulate.m button in the toolbar.* When running this file, four files are written in a folder named Results (in a format compatible with Microsoft Excel) that includes calculated mechanism output at each crank link rotation increment The four files are described in Table G.12 Also, when running RRRR_Spherical_Simulate.m, a graphical user interface appears where 4R Spherical mechanism motion is simulated in motion over the defined crank rotation range.† To replay this simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) * This button is a green triangle (over a white square) and the text Run RRRR_Spherical_Simulate.m appears when the cursor is over it † The link chord lengths, rather than the arced links themselves, appear in the 4R Spherical mechanism simulation 340 Appendix G: User Instructions for MATLAB® and SimMechanics® Files TABLE G.12 Output Files from Appendix G.6 MATLAB® and SimMechanics® Filesa Filename Contents (See Figure G.12 for Mechanism Reference) p1_disp.csv q1_disp.csv r1_disp.csv ub0_ang_disp.csv X, Y, and Z coordinates of coupler point p1 X, Y, and Z coordinates of coupler point q1 X, Y, and Z coordinates of coupler point r1 Angular displacement (in degrees) about joint axis ub0 a The mechanism output in these files is written for each increment of the crank rotation range defined in rows 23 through 25 in RRRR_Spherical_Simulate.m Rigid-body variables (e.g., p1, q1, r1) b1 a1 Y X Z a0 ub0 b0 FIGURE G.12 4R Spherical mechanism When using values ±0.1, ±0.01, or ±0.001 for step_ang in the file RRRR_ Spherical_Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) G.7 RSSR-SS MECHANISM Appendix G.7 folder (which is available for download at www.crcpress.com) includes three MATLAB and SimMechanics files for the kinematic analysis and simulation of RSSR-SS mechanisms These three files are described in Table G.13 To conduct a kinematic analysis, the user specifies the mechanism link dimensions and the crank motion parameters in the file RSSR_SS_Simulate.m Values are specified for link variables a0, a1, b0, b1, ua0, ub0, c0, c1, p1, q1, and r1, respectively Additionally, values are specified for the initial crank angle (start_ang), the crank Appendix G: User Instructions for MATLAB® and SimMechanics® Files 341 TABLE G.13 Appendix G.7 MATLAB® and SimMechanics® Files Filename RSSR_SS_Prepare.m RSSR_SS_Model.mdl Post_Simulation_Task.m Use of File To specify mechanism link dimensions and crank link controls To calculate mechanism output and simulate mechanism motion To write mechanism output (compatible with Microsoft Excel) % % Here, values for the RSSR-SS mechanism variables a0, ua0, a1, % b0, ub0, b1, c0, c1 and coupler points P1, Q1 and R1 are % assigned a0 = [0, 0.0230, –0.0791]; ua0 = [0.2705, 0.0800, 0.9594]; a1 = [–0.4508, 1.9500, –0.1127]; b0 = [0.8236, 0.2848, –0.2711]; ub0 = [0.5965, 0.1729, 0.7838]; b1 = [0.8097, 2.6941, –0.7919]; c0 = [0, 0, –1]; c1 = [–0.4655, 1.7992, –1.3256]; P1 = [–1.1176, 3.8219, –0.9088]; Q1 = [0.3947, 2.8777, –0.7801]; R1 = [–0.5918, 2.6499, –1.1277]; % % % Here, values for the start, step and stop displacement angles % for the crank link are assigned start_ang = 0; step_ang = 30; stop_ang = 360; % - FIGURE G.13 Sections of RSSR_SS_Simulate.m with sample values given in bold rotation increment (step_ang), and the final crank angle (stop_ang), respectively Figure G.13 illustrates the user input sections of the file RSSR_SS_Simulate.m with sample values given in bold.* After specifying the mechanism dimensions and driving link parameters in the file RSSR_ SS_ Simulate.m, the next step is to run this file To run the file, the user can use the “F5” button or the Run RSSR_ SS_ Simulate.m button in the toolbar.† * Only positive or negative integer values should be specified for start_ang and stop_ang The authors recommend minimum values of ±1, ±0.1, ±0.01, or ±0.001 for step_ang † This button is a green triangle (over a white square) and the text Run RSSR_SS_Simulate.m appears when the cursor is over it 342 Appendix G: User Instructions for MATLAB® and SimMechanics® Files TABLE G.14 Output Files from Appendix G.7 MATLAB® and SimMechanics® Filesa Contents (See Figure G.14 for Mechanism Reference) Filename p1_disp.csv q1_disp.csv r1_disp.csv ub0_ang_disp.csv a X, Y, and Z coordinates of rigid-body point p1 X, Y, and Z coordinates of rigid-body point q1 X, Y, and Z coordinates of rigid-body point r1 Angular displacement (in degrees) about joint axis ub0 The mechanism output in these files is written for each increment of the crank rotation range defined in RSSR_SS_Simulate.m Rigid-body variables (e.g., p1, q1, r1) b1 c1 a1 c0 ub0 b0 Y a0 X ua0 Z FIGURE G.14 RSSR-SS mechanism When running this file, four files are written in a folder named Results (in a format compatible with Microsoft Excel) that includes calculated mechanism output at each crank link rotation increment The four files are described in Table G.14 Also, when running RSSR_ SS_ Simulate.m, a graphical user interface appears where RSSR-SS mechanism motion is simulated in motion over the defined crank rotation range.* To replay this simulation, the user could select “Simulation” in the top menu of this GUI and then “Start” in the drop-down menu (or use “Ctrl+T”) * The passive DOF in the S-S link must be eliminated to produce a working RSSR-SS simulation in SimMechanics® To achieve this, a massless S-S link (which is not visible in a simulation) is used As a result, the S-S link does not appear in the RSSR-SS simulation Appendix G: User Instructions for MATLAB® and SimMechanics® Files 343 When using values ±0.1, ±0.01, or ±0.001 for step_ang in the file RSSR_SS_ Simulate.m, it would be helpful to modify start_ang and stop_ang to produce a smaller crank rotation range Doing this will reduce the solution calculation time and the amount of data written to the output files We recommend the user begins with a step_ang value of ±1 and progresses to the smaller values (with correspondingly smaller crank rotation ranges) MACHINE DESIGN Mechanism Design Visual and Programmable Approaches In the field of mechanism design, kinematic synthesis is a creative means to produce mechanism solutions Combined with the emergence of powerful personal computers, mathematical analysis software and the development of quantitative methods for kinematic synthesis, there is an endless variety of possible mechanism solutions that users are free to explore, realize, and evaluate for any given problem in an efficient and practical manner Mechanism Design: Visual and Programmable Approaches provides a broad introduction to kinematic synthesis, presenting and applying motion, path, and function generation methodologies for some of the most basic planar and spatial single- and multiloop linkage systems This work provides numerous in-chapter synthesis examples and end-of-chapter synthesis problems Users can also invent their own specialized synthesis problems according to their particular interests The commercial mathematical software package MATLAB® and its mechanical system modeling and simulation module SimMechanics® are thoroughly integrated in this textbook for mechanism synthesis and analysis The reader is therefore enabled to readily apply the design approaches presented in this textbook to synthesize mechanism systems and visualize their results With this knowledge of both kinematic synthesis theory and computer-based application, readers will be well-equipped to invent novel mechanical system designs for a wide range of applications K16470 an business w w w c r c p r e s s c o m 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK w w w c rc p r e s s c o m