Adaptation of the Paddle-One

Transcription

1 Adaptation of the Paddle-One Putting some into your paddling machine. Richard E. Bring balance and fun to your paddlesport training! January Adaptation of the Paddle One Revision B 2010 Richard Butts Page 1

2 Contents Project Overview... 3 Deciding on an Appropriate Radius for the Rocker... 5 Recognizing the Critical Rocker Radius... 5 Diagram of a Rocker having a Radius that will be Stable and one that will be Unstable Determining the appropriate Rocker Radius A Rocker Design for the 2002 Paddle One Bill of Materials, Tools and Suggestions for the 2002 Paddle One... 8 Lean Rocker Assembly Sequence for the 2002 Paddle One... 9 CAD drawing of the 2002 Paddle One with Rockers Installed Dimensions of the Rocker s Bottom Half for the 2002 Paddle One, Qty Dimensions of the Rocker s Top Half for the 2002 Paddle One, Qty Dimensions of the Side Panel for the 2002 Paddle One, Qty Dimensions of the Spacers for the 2002 Paddle One, Qty Dimensions of the Rocker Support, Qty A Rocker Design for the Current Paddle One Bill of Materials, Tools and Suggestions for Current Paddle One CAD drawing of the Current Paddle One with Rockers Installed Photos of the Rocker Assembly on the Current Paddle One Lean Rocker Assembly Sequence for the Current Paddle One Dimensions of the Rocker s Bottom Half for the Current Paddle One, Qty Dimensions of the Rocker s Side Panel for the Current Paddle One, Qty Dimensions of the Spacer for the Current Paddle One, Qty Parts common to the Current Paddle One Rocker and the 2002 Paddle One Rocker Views of the Early Leaner Versions The Stock Paddle One, about 2002 vintage The Elevated Paddle One The First Leaner on Foam Rubber Blocks Travel Limit Blocks from an Automobile Suspension plus Foam Rubber Blocks Upside-Down Caster Upside-Down Caster with Foam Rubber Blocks Pair of Upside-Down Casters with Rocker The First Rocker The Final Rocker Comparing the First Rocker to the Final Rocker for the 2002 Paddle One The Secondary Stability Support The Counter-Balance Weight Modification of the Drag Strap Loading Addition of a Bicycle Speedometer Adaptation of the Paddle One Revision B 2010 Richard Butts Page 2

3 A Leaning Design for the Paddle One Applied to the 2002 Paddle One and to the current Paddle One Project Overview The Paddle One machines are terrific for exercising the strength and coordination used in canoe and kayak paddling. I own an older Paddle One canoe version and the arm, torso and leg motions feel very similar to real paddling. A significant difference between the Paddle One and real paddling is the inability to lean the Paddle One. This report provides photos plus assembly and detail drawings of the leaning adaptation I made for my 2002 Paddle One and the one I made for the current Paddle One. The Paddle One in most of these photos is my older one, about 2002 vintage. My interest in being able to lean the paddling machine comes from three sources 1) coordinated movement of the hips, arms, legs and torso is important for balancing and steering a canoe so training the balancing skill is appropriate. 2) I have a lack of symmetry when it comes to leaning right vs. leaning left. I have no idea if my lack of leaning symmetry is any more or any less than the average person. Paddling requires symmetry and while paddling I notice my symmetry could be better. The leaning paddling machine allows me to work on discovering the joints, ligaments, motions, coordination, etc. that limit my symmetry and that gives me the opportunity to make improvements. 3) With the machine free to lean it is even more fun to use! My completed 2002 leaning Paddle One looks like this: The adaptation shown is easily made from 2 x 4 dimensional lumber and ¼ plywood. You must be aware that if you build and use the adaptation you will be able to fall off the machine if you lean farther than your skill allows you to recover. You are responsible for safety while making and while using the adaptation. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 3

4 The following pages show the materials, tools and parts I used for making a leaning adapter for the Paddle One. If you find an error, missing dimension or have a suggestion about this project please contact me. The development of the adaptation took several iterations. The early versions are shown along with a brief description of how I arrived at each and why I moved on to the next. The final version is easy to make, easy to understand how it performs and easy to install. The installation is a slip-on design. There is no need for clamps or fasteners to hold the rocker onto the Paddle One. I considered and experimented with adding hard stops to limit the amount of lean. The motivation was to prevent falling off. Falling off sounds worse than it is. Typically it means taking a foot off the peg and putting it onto the floor. Even so, there is nothing except your skill preventing a slip off the seat and a bump on the floor. With hard stops it was apparent the potential for falling off was greater than without the hard stops. The reason is inertia. While paddling on the machine there will be occasional leans that are too quick and are going too far. At the moment one occurs, I and the machine are both rotating towards falling off but we haven t gotten there yet. When I hit a hard stop the machine stops moving but my body doesn t. So I keep going and fall off anyway. Without the hard stops I found I could recover from most leans better than with the hard stops. I also tried soft stops in the form of shock cords. When they are stiff enough to effectively slow the leaning mass in an extreme lean they are also stiff enough to prevent the fun of the small lean. Soft stops weren t much of an advantage and seemed an unnecessary addition. The simplest, most effective way to keep the small leans lively and slow the large leans is to create a large radius rocker. Another, less simple, way to do it is to set the rocker (an outside radius) on a curved surface (an inside radius) the radius of which is larger than the rocker s radius. I call it a secondary stability support and there is a photo of that setup in the early versions section of this report. There are two other modifications I made to my Paddle One. I changed the method of loading the flywheel s drag strap and I added a speedometer. There are photos of both modifications. You re welcome to use these designs for any non-commercial purpose. If you make one, you have the responsibility for the quality and care with which you make it, the quality and care with which you attach the Paddle One to it and the suitability of the whole system for any use it is put to. I hope you find this information useful. Enjoy and train safely. Rich Butts, Mechanical Engineer January 2010 richeb@frontiernet.net This design is drawn in Sketch-Up v7. If you want the model files, contact me. If you have a project design that you d like drawn up or analyzed you re invited to contact me with your needs * * * * * * * Adaptation of the Paddle One Revision B 2010 Richard Butts Page 4

5 Deciding on an Appropriate Radius for the Rocker Recognizing the Critical Rocker Radius Determining an appropriate radius for the rocker is made easier by recognizing three elements of the leaning process: 1) When the machine and rocker are leaned the rocker rolls on the floor. (The rocker does not pivot about a fixed location.) 2) When the rocker rolls on the floor the center of the rocker s radius is always vertically over the rocker s contact point with the floor. 3) When a person returns to the center position after leaning the machine they have made the return happen by keeping their composite (machine and self) center of gravity between the neutral (i.e. no-lean) position and the vertical line containing the rocker s center. When a person leans the machine and remains balanced they have located their composite center of gravity on the vertical line containing the rocker s center. When a person leans the machine and uncontrollably continues to lean they have located their composite center of gravity outboard of the vertical line containing the rocker s center. The critical radius for stability is the one which places the rocker s center at the seat height. A center point above the seat height will be most stable. A center point below the seat height will be least stable. Human anatomy and the limits of our ability to tilt the pelvis relative to the torso and to then dynamically manage that tilt to achieve balance are the reasons that is true. Stable Rocker Radius Critical Rocker Radius Seat Height Unstable Rocker Radius Very Stable Very Unstable Adaptation of the Paddle One Revision B 2010 Richard Butts Page 5

6 Present day Paddle One - seat height, Paddle One - seat height, 9 ½ Hip-to-Torso Angle at Balance Composite Center of Mass At Balance Diagram of a Rocker having a Radius that will be Stable and one that will be Unstable. Return-to-Neutral Torque due to Center of Mass Location Hip-to-Torso Angle at Balance Composite Center of Mass (Person and Machine) When trying to balance Make-You-Fall-Off Torque due to Center of Mass Location Composite Center of Mass (Person and Machine) When trying to balance Composite Center of Mass At Balance The diagram on the left shows the stabilizing effect caused by choosing a rocker radius larger than the seat height. The diagram on the right shows the de-stabilizing effect caused by choosing a rocker radius smaller than the seat height. To achieve balance in either configuration the center of mass must be positioned on the vertical line passing through the rocker s center. While seated the center of mass location is mostly controlled by the upper body. At the balance position the small radius rocker forces a larger angle between hips and upper body than will be needed with the large radius rocker. Difficulty in achieving and maintaining that larger angle makes the small radius rocker less stable. To determine the rocker radius that will give us a stable design we need to know the height of the seat. The present day Paddle One is much taller than the 2002 Paddle One. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 6

7 Determining the appropriate Rocker Radius. The diagram on the right will help to determine the critical rocker radius: Solving this equation will give us the critical rocker radius. R Critical - Current Rocker = 20.7 R Critical Rocker = 14.1 R rocker 17 (current design) 9 ½ (2002 design) 12 ½ 2 ¾ (current design) 3 3 / 16 (2002 design) For best stability I recommend a rocker radius of 22 minimum for the current Paddle One and 14 1 / 8 minimum for the 2002 Paddle One. I ve added an extra inch and a quarter to the rocker radius for the current Paddle One to keep any quick, large lean recoverable even with the machine s high center of gravity. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 7

8 A Rocker Design for the 2002 Paddle One. Bill of Materials, Tools and Suggestions for the 2002 Paddle One Bill of Materials Rocker Bottom, Qty x 4 x 16 ½ Dimensional Lumber Rocker Top, Qty x 4 x 16 ½ Dimensional Lumber Side Panels, Qty ¼ x 16 ½ x ¼ Plywood Spacers, Qty ¼ Plywood Rocker Top Support, Qty x 4 x 12 ½ Dimensional Lumber Rocker Bottom Support, Qty x 6 x 12 ½ Dimensional Lumber 1 Wood Screws or Drywall Screws, Qty (for fastening the sides to the rocker) Wood Glue, Qty A/R... (as required, for fastening the spacers to the rocker) Tools Tape Measure Carpenters Square 1 / 16 Drill Bit... (pilot holes for the screws) Saw... (Hand, Table, Jig or Band whatever suits you. I used a band saw and a table saw.) Drill... (I used a battery powered portable) Large Compass, up to ~14 radius... (I used a non-stretch string, a thumbtack and a pencil) Suggestions To get a good glue joint between the Rocker-Bottom and the Rocker-Top I used a table saw to cut 1 / 8 off the long side of the 2 x4 x16½ so the faces were flatter than the dimensional lumber surface. You ll see the 2 x 4 dimensions shown as 1 ½ x 3 3 / 8. Those dimensions come from the 1 ½ x 3 ½ true dimensions minus the 1 / 8. When assembling the rocker, spacer and side panels it was awkward to hold all the pieces in place while drilling pilot holes and inserting screws. Instead I glued the spacers in place, let the glue set-up then fastened the side panels with screws. After cutting the 14 1 / 8 radius curve in the Rocker-Bottom I gave the curve a smooth, bump free finish by using a belt sander. The rockers roll smoothly and easily when sitting on the wide side of a 2 x4. That s why the Rocker-Top Support and Rocker-Bottom Support get stacked-up, glued together and used. I ve never tried using the rockers on a rug only. That might be OK too. I always use the paddling machine and the supports on a rug instead of a potentially slippery hard floor. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 8

9 Lean Rocker Assembly Sequence for the 2002 Paddle One 1 For 2 x4 rocker construction - Glue the pieces together. Rocker - Top Rocker - Bottom 2 Glue the spacers in place. 3 Screw the side panels in place. Notice there are 6 screws on each side. The markings on each panel locate screws on opposite sides of the rocker and ½ offset from each other so they don t collide. Spacers Side Panels Adaptation of the Paddle One Revision B 2010 Richard Butts Page 9

10 CAD drawing of the 2002 Paddle One with Rockers Installed Early Paddle One, about 2002 vintage. Rocker Assembly Rocker Support Adaptation of the Paddle One Revision B 2010 Richard Butts Page 10

11 Dimensions of the Rocker s Bottom Half for the 2002 Paddle One, Qty 2 Adaptation of the Paddle One Revision B 2010 Richard Butts Page 11

12 Dimensions of the Rocker s Top Half for the 2002 Paddle One, Qty 2 My Paddle One has the base made of square steel tubing 2 x 2 x 12 ½ (including the plastic end cap). This opening is made to fit it. Your Paddle One may be different. You should check this and adjust accordingly. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 12

13 Dimensions of the Side Panel for the 2002 Paddle One, Qty 4 This feature is for holding a counterbalance weight on the front rocker. It is not needed on the rear rocker. You may need to adapt its size to the weight you use. The red locations are for screws in one panel and the blue locations are for screws in the opposing panel. This avoids collisions between screws on opposite sides. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 13

14 Dimensions of the Spacers for the 2002 Paddle One, Qty 12 Adaptation of the Paddle One Revision B 2010 Richard Butts Page 14

15 Dimensions of the Rocker Support, Qty 2 Adaptation of the Paddle One Revision B 2010 Richard Butts Page 15

16 A Rocker Design for the Current Paddle One Bill of Materials, Tools and Suggestions for Current Paddle One Bill of Materials Rocker Bottom, Qty x 4 x 16 ½ Dimensional Lumber Rocker Top, Qty x 4 x 16 ½ Dimensional Lumber Side Panel, Qty / 32 x 16 ½ x ¼ Plywood Spacers, Qty mm Lauan Plywood Rocker Top Support, Qty x 4 x 12 ½ Dimensional Lumber Rocker Bottom Support, Qty x 6 x 12 ½ Dimensional Lumber 1 Wood Screws or Drywall Screws, Qty (for fastening the sides to the rocker) Wood Glue, Qty A/R... (as required, for fastening the spacers to the rocker) Tools Tape Measure Carpenters Square 1 / 16 Drill Bit... (pilot holes for the screws) Saw... (Hand, Table, Jig or Band whatever suits you. I used a jig saw and a table saw.) Drill... (I used a battery powered portable) Large Compass, up to ~22 radius... (I used a non-stretch string, a thumbtack and a pencil) Suggestions To get a good glue joint between the Rocker-Bottom and the Rocker-Top I used a table saw to cut 1 / 8 off the long side of the 2 x4 x16½ so the faces were flatter than the dimensional lumber surface. You ll see the 2 x 4 dimensions shown as 1 ½ x 3 3 / 8. Those dimensions come from the 1 ½ x 3 ½ true dimensions minus the 1 / 8. When assembling the rocker, spacer and side panels it was awkward to hold all the pieces in place while drilling pilot holes and inserting screws. Instead I glued the spacers in place, let the glue set-up then fastened the side panels with screws. After cutting the 22 radius curve in the Rocker-Bottom give the curve a smooth, bump free finish by using a belt sander. The rockers roll smoothly and easily when sitting on the wide side of a 2 x4. That s why the Rocker-Top Support and Rocker-Bottom Support get stacked-up, glued together and used. I ve never tried using the rockers on a rug only. That might be OK too. I always use the paddling machine and the supports on a rug instead of a potentially slippery hard floor. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 16

17 CAD drawing of the Current Paddle One with Rockers Installed Current Paddle One Rocker Assembly Rocker Support Adaptation of the Paddle One Revision B 2010 Richard Butts Page 17

18 The rocker being slipped onto the Paddle One Frame. The rocker on the Paddle One Frame. Photos of the Rocker Assembly on the Current Paddle One The assembled rocker. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 18

19 Lean Rocker Assembly Sequence for the Current Paddle One 1 For 2 x4 rocker construction - Glue the pieces together. Rocker - Top 2 Glue the spacers in place. Rocker - Bottom Spacers 3 Screw the side panels in place. Notice there are 6 screws on each side. The markings on each panel locate screws on opposite sides of the rocker and ½ offset from each other so they don t collide. Side Panel Adaptation of the Paddle One Revision B 2010 Richard Butts Page 19

20 Dimensions of the Rocker s Bottom Half for the Current Paddle One, Qty 2 Adaptation of the Paddle One Revision B 2010 Richard Butts Page 20

21 Dimensions of the Rocker s Side Panel for the Current Paddle One, Qty 4 The red locations are for screws in one panel and the blue locations are for screws in the opposing panel. This avoids collisions between screws on opposite sides. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 21

22 Dimensions of the Spacer for the Current Paddle One, Qty 12 Adaptation of the Paddle One Revision B 2010 Richard Butts Page 22

23 Parts common to the Current Paddle One Rocker and the 2002 Paddle One Rocker Rocker Top, Qty 2 See page 12 for dimensions Rocker Top Support, Qty 2 Rocker Bottom Support, Qty 2 See page 15 for dimensions Adaptation of the Paddle One Revision B 2010 Richard Butts Page 23

24 Views of the Early Leaner Versions The Stock Paddle One, about 2002 vintage I have a Paddle One which is several years old. I do not know the date of manufacture. I guess the date to be about years. The machine has a low-to-the-floor seat height. It is about 9 1/2 (24.1cm) from floor to the seat s front edge. The low seat height made it very easy to strike the floor with the end of the paddle s shaft. The floor to foot-peg height was also a little too short. By the way, today s Paddle One is taller than the vintage I have. A 2008 model Paddle One has a 17 height from floor to the seat s front edge. One of the first adaptations was to raise the machine up. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 24

25 The Elevated Paddle One Raising the machine by 3 inches (7.6cm) is enough to keep the paddle shaft away from the floor and put the foot pegs at a comfortable level. The lift is provided by a 2 x 4 board on top of a 2 x 6 board. Actual dimensions of these boards is 1 ½ x 3 ½ and 1 ½ x 5 ½ respectively. I went with this for awhile and then came across some dense foam rubber that gave me an idea about a simple way to get the machine to lean. The First Leaner on Foam Rubber Blocks With the machine sitting on dense foam blocks at all four corners it gained a simple ability to lean. The lean was small, just a few degrees when the base kept contact with the foam. Leaning further lifts one end of the base off the foam. That effect was a moving pivot point and it caused the lean to feel un-boat-like. So next I put in a fixed pivot. By the way, the foam blocks have a nice characteristic in that the lean has 3 distinct phases: 1) an initial phase where the lean is small while the foam compresses on one side and expands on the other, 2) a somewhat self limiting phase where the base of the machine acts as an outrigger support which is farther off-center than the machine and the paddler s center of mass and 3) the can t-go-no-mo phase where the base begins to slowly slide off the foam. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 25

26 Travel Limit Blocks from an Automobile Suspension plus Foam Rubber Blocks I m fortunate to live an area that has all four seasons. The seasons bring many nice things but they also bring the roadway pothole. In my area salt is used to manage roadway ice. The salt handles the ice well. It also helps cars decompose with rust while still in use. Together the potholes and rust give us roadways scattered with the occasional car part. Frequently the part is a hard rubber travel limit block from a suspension. I used a pair of them to make a fixed, central pivot to lean about. The top of the pivot is just slightly higher than the foam block. When leaning the paddling machine the pivot point stays centered and the foam compresses to resist the lean. This setup gives a nice, progressive feel to the lean. It is more rigid than a real boat, the available lean is not enough and a large lean causes the pivot point to move out to the end of the base. Better but not quite there yet. Upside-Down Caster I used a short piece of 2 x4 and made a frame that fit the base then shaped a semi-circle that fit the wheel of a caster. With the caster upside-down, the pivot point was now fixed in position relative to the paddling machine. The amount of available lean was much larger and there was no change in lean resistance due to compressing foam or a moving pivot point. This was a nice idea but I could not stay upright on this. I could not paddle because I could not even sit still and stay upright. It is very much too fast. This photo shows cut-outs where you ll see I subsequently put the foam. The original frame did not have those cut-outs because I wanted to do away with the foam. So on to slowing it down by bringing back the foam. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 26

27 Upside-Down Caster with Foam Rubber Blocks Bringing back the foam slowed down the responsiveness to a reasonable level. I used this setup for a long time. It has a nice progressive feel to the lean but the available lean is less than I want. Leaning a lot can still cause the pivot to transition from the caster to the outboard end of the frame. So better but not best. I ran out of ideas for variations on this theme. So it was time to go in a different direction. Pair of Upside-Down Casters with Rocker So, if one caster is OK then two should be even better! That turned out to be not true. This idea was too unstable. The rocker does not neatly roll on each caster. Instead it will roll a short distance, until the center of mass of the paddler & paddling machine are outside the caster then the rocker lifts off the opposite caster and the whole unit falls over along with me too!. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 27

28 The First Rocker This is the first rocker I made. It turned out to be too responsive. It is possible to use it and paddle but it took all my focus to stay upright. This rocker didn t add fun to using the paddling machine so I didn t want to stay with it. I made this pair of rockers out of a scrap piece of 2 x 12 dimensional lumber. After sketching an arc that I thought would work it took only a little time with a big compass made of string, a pencil and 30 minutes at a band saw to make a pair. The Final Rocker In the second rocker I made the radius larger to slow it down and I also lowered the paddle machine by ¾ (19mm). The lowering helped slow the response but mostly it put the frame deeper into the rocker and that held it in place better. The second rocker is very comfortable to lean with. It has a large range of lean available and the lean sensation is very similar to being in a solo canoe. The photo shows the rocker with the sides in place. The sides keep the Paddle One base centered on the rocker front-to-back. There are no fasteners holding the rocker onto the Paddle One. The rocker slips into place and it stays put. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 28

29 Comparing the First Rocker to the Final Rocker for the 2002 Paddle One Here you can see the difference between the first rocker and the final rocker. The first one is the one on top. The final one, on the bottom, shows the difference in the radii of the two rockers. The first one s radius is 9 5/8 (24.4cm), the final one s radius is 14 1/8 (35.9cm). It doesn t look like much difference but it is when you re sitting in the seat. The radius change, along with a ¾ lowering of the machine makes for a much more comfortable leaning sensation while paddling. The Secondary Stability Support I discovered it is possible to have easy leaning near the neutral position and difficult leaning near the far lean positions. To get that effect I put the 14 1 / 8 rocker on top of the 22 radius cut-off (i.e. scrap) piece. This is a handy solution for two people using one machine when they have different balance abilities just slip the large radius pieces in The rocker on top of the secondary stability support. or out. The secondary stability support. 2 are required, one under each rocker. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 29

30 The Counter-Balance Weight Now that the paddling machine can lean side-to-side the off-center flywheel will tilt the machine. To counter that and make the machine level I added a 1 ½ pound (0.7kg) dumbbell at the end of the rocker. The current Paddle One has a smaller and more centered flywheel so the counterweight isn t needed. Modification of the Drag Strap Loading The original drag strap tensioner is a shock cord fastened to the frame. It is the green object in the photo. The drag strap was attached to it and wrapped from the bottom to the top of the flywheel (counter-clockwise in the photo). The drag resistance adjustment was done by putting more or less of the drag strap s tail through a clamp mounted to the frame. Put more through and the shock cord is stretched putting more tension in the wrap. I disconnected the shock cord and hung a dead-weight on the strap. In the photo the dead-weight is the blue bag and it is filled with about 1 pound (0.45 kg) of sand. The drag resistance is now more consistent day to day and during each work-out. Since the machine leans I also added a guide to keep the deadweight from freely swinging side-to-side. The guide is a common wire coat hanger with the hanging hook bent closed. The photo shows the guide attached to the rocker and extending out to the dead-weight. Adaptation of the Paddle One Revision B 2010 Richard Butts Page 30

31 Addition of a Bicycle Speedometer I like to have a quantitative way to know the effort I m putting into paddling the machine so I added a bicycle speedometer to the flywheel. The speedometer has a non-contact magnet/sensor shown in the right photo. The left photo shows the mounting of the display on the frame and in front of the foot pegs. (The white item in the photo is a timer.) Adaptation of the Paddle One Revision B 2010 Richard Butts Page 31