Classic Rocker
Optimal Design
Team 7
NSF – Legless Rocker
Project Coordinator: Dr. Brooke Hallowell
Supervising Professor: Dr. John Enderle
11/11/05
Tom Dabrowski
Sarah Philo
Adam Rauwerdink
I. Discussion
Objective
The goal of this project is to design and implement a mechanism to automate the rocking motion of a legless rocking chair. This will be achieved through the use of a motor and cam system to apply the necessary forces at the back of the chair. Initiation of the rocking motion will be through a simple user-operated switch. The user will also have the ability to control a built-in sound system. For safety, caretakers will have master control over the rocking motion as well as the audio system.
The design being considered for the rocking mechanism will require that the legless rocker have a steel frame that will be able to withstand the forces created during rocking. As most legless rockers have cheap plastic frames, the number of rockers of acceptable structural strength will be limited. The rocker will be attached to a metal frame that will sit on the ground and extend from level with the front edge of the rocker to slightly past a vertical line from the top-back of the chair. The chair will be attached to this by a hinge system which the chair will rock on. To the back end of the frame a gearmotor will be attached. A cam system and linkage bar will be connected to this motor. These will provide the necessary forces for rocking.
The interchangeable controls for the user will be a touch pad and a squish switch. These controls will give the user the ability to start and stop the rocking motion and to turn on and off the sound in a fashion similar to a mute button. The caretaker will have master control over all aspects of the chair. The master controls will be on the back of the chair, out of reach of the user. These controls will include a switch to control the rocking motion, and access to the CD player including controls for power, mute, volume, and track. For safety reasons, there will be a master switch that will cut power to the entire chair, and may be a keyed switch or remote control.
The audio component will be powered by a basic car CD player. This will provide amplification for the sound as well as anti-skip capabilities to limit CD skipping as the chair rocks. The CD player will be installed in a ‘control tower’ behind the chair. Speakers will be built into the headrest.
The chair will use power from a standard 120 volt wall socket via an electric cord. A battery system was considered, but the high amperage of the motor meant that the battery would either need to be charged frequently or be excessively large and therefore heavy. These factors would drastically lower ease of use of the chair. Because the CD player and motor both run off of 12VDC, a power supply of proper wattage like those in a computer will need to be installed. An automatic cord reel, like in a vacuum cleaner, is a consideration. This would allow the external cord length to be kept to a minimum, also it would protect against damage to the internal connections of the chair, as someone yanking on the cord would pull out more cord rather than breaking the internal electrical connections of the chair.
The final unit will be a self-contained, easily moveable chair with all electrical and mechanical parts guarded as best as possible.
Figure 1: Finished Chair Side View
Figure 2: Chair 3D View
SUBUNITS
Frame
The rocker frame will consist of two parts: the external frame on the ground and the internal frame reinforcing the legless rocker. The external frame will provide an attachment point for all parts of the rocking mechanism. The internal frame will provide the purchased legless rocker with additional rigidity and strength so that it can handle the forces placed on it by the rocking mechanism.
The external frame will include a metal base that will lie on the ground, a metal hinge that will tie the frame and legless rocker together, and a riser on the front edge of the frame. The metal for the frame can be obtained from Yarde Metals in Southington, CT [1]. The base will be built from metal, and will be approximately 40” long and 22” wide. The exact dimensions will depend on the size of the legless rocker chosen. The width of the base will be approximately the width of the rocker, and the length is, at minimum the distance between the front edge of the rocker at its most upright position and the top-back of the chair at its most reclined position. The length may also need to be increased by a few inches if more room is needed for the motor attachment.
The chair will be joined to the base by a large hinge that will ideally run the full width of the chair. The two attached faces of the hinge will be parallel to each other when the chair is upright and will rotate about a pivot in the middle. The hinge will need to be strong enough to hold the combined weight of both the chair and user, and will have to be constructed of a material strong enough to support said weight. A pre-built hinge of this kind has not yet been found, so a drawing of the basic design, which could be built in the machine shop, has been included.
Figure 3: Hinge Design
On the front edge of the base, a metal riser will be attached. The top of this riser will abut the bottom of the rocker at its most upright position. The purpose of this riser will be to prevent the application of a large force on the motor assembly when a user rests on the front edge of the rocker. This will ensure that the overhung load rating of the motor is not surpassed. It will be important to keep the riser from infringing on the motion of the chair, so it will need to be positioned carefully. Another metal riser will be placed behind the chair so that if the cam link breaks, the chair will rest on the riser and not tip over.
The design of the internal frame will be dependent on the existent frame in the purchased legless rocker. Framing will need to be placed at the location of both mechanical attachments: the hinge and linkage bar. Additional framing may also be necessary to ensure that the chair does not break at the junction of the back and seat. The forces applied by the rocking mechanism will create a moment about this point which could lead to the chair frame bending and ultimately failing. The back and bottom of the chair will likely need to be opened in order to accomplish the required strengthening of the frame. The ease at which the required frame work could be accomplished will need to be considered when the pre-built legless rocker is chosen.
Rocking Forces
An analysis of the forces of rocking was performed using a scaled drawing in Visio and a scale model in Working Model 2D. The legless rocker dimensions were taken off of Linen n’ Things website [3]. The chair used, the “Attitude Video Rocker”, has a solid wooden frame, a key component for our design. The dimensions given for the chair were 31 inches high, 22 inches wide, and 34 inches deep. This chair was found at a local Linen n’ Things store and the structural integrity of the frame in the critical lower sections of the chair was confirmed.
Figure 4: ‘Attitude’ Video Rocker
Analysis of this chair found that during comfortable rocking the back of the chair moved a horizontal distance of seven (7) inches from its normal position. This value is used for the following analysis.
With the chair dimensions and a value for the travel distance during rocking, a scaled drawing could be made in Visio. These drawings, along with anthropomorphic data from Dr. John Enderle’s Introduction to Biomedical Engineering textbook [4], allowed for summation of the forces acting upon the chair to be calculated. The segment weight and center of mass were determined for the upper body, thigh, and lower leg. Dr. Hallowell provided information to us that patient weights would vary from 80-190 pounds. To be safe, 300 pounds was used as the maximum weight in the performed calculations.
Trunk, arm, head / Thigh / Foot and LegSubject Weight (lbs) / Center of mass / Weight (lbs) / Center of mass / Weight / Center of mass / Weight
80 / 0.626 / 54 / 0.433 / 16 / 0.606 / 10
300 / 0.626 / 204 / 0.433 / 60 / 0.606 / 36
Table 1: Anthropometric data
Figure 5: Chair fully upright
Figure 6: Chair at midpoint of rocking motion
Figure 7: Chair fully reclined
UPRIGHT ANALYSIS
MIDDLE ANALYSIS
RECLINED ANALYSIS
The above calculations show the relationship between the placement of the hinge and the force applied at the attachment point of the linkage bar on the back of the chair. Calculations in the initial design II were completed for two conditions: legs outstretched and legs resting on the ground. Upon analysis of a person using the rocker at the Linens n’ Things store is what found that it would be unlikely for one’s legs to be off of the ground. Further calculations were then done in Microsoft Excel to determine which hinge position resulted in the smallest maximum force at the linkage bar attachment point.
Position / x upright / x reclined / x middleFulcrum Distance / 11.00 in / 17.50 in / 14.50 in
Force / -48.00 lb / 91.39 lb / -12.52 lb
Table 2: Excel Analysis of Optimal Hinge Position
The analysis found that the smallest maximum force occurred when the hinge was placed 11 inches from the back of the chair at its upright position. The greatest force exerted by the linkage bar at this hinge position was 91.39 pounds when the chair was at its most reclined position. These forces will be important later in this report (Cam and Linkage Bar section), as they will be used to calculate the torque required by the gearmotor. The highest force is important, as gearmotors have an overhung load rating. This rating limits the amount of force that can be applied perpendicular to the motor shaft. The riser on the front edge of the entire system’s base will act to prevent the chair from rocking too far forward so that the overhung load rating is not surpassed.
Cam and Linkage Bar
The forces required for rocking will be transferred from the motor to the chair by a two part system consisting of a cam and linkage bar. The cam, with its diameter dependent on the placement of the motor, will be cylindrical in shape and be attached through its center to the shaft of the motor. A linkage bar, with its length dependent on the placement of the motor, will connect the back of the chair to a point on the cam. This system will translate the rotational motion of the motor into linear motion of the chair. The exact size and position of this system will influence the torque requirements of the motor. The following analysis determines all of these unknown factors.
The forces determined earlier in this report from the free body diagrams of the chair assumed that the linkage bar forces were in the vertical direction only. This is not the case, though, as the linkage bar supplies both vertical and horizontal forces. For this reason the moment required to balance the chair is what needs to be provided by the linkage bar. This moment, as well as the vertical and horizontal distances to the applied force, varies with the chair position and is dependent on the linkage bars attachment point. For the sake of safety and to keep the linkage bar short it is being attached to the chair at a position 4” up from the bottom of the chair.
x upright / x reclined / x middlemoment leg / -432.00 / 913.85 / -118.91 / in-lb
vertical / 4.00 / 2.00 / 3.00 / in
horizontal / 9.00 / 10.00 / 9.50 / in
Table 3: Moments and distances at different chair positions
The position of the motor and therefore the position of the cam will determine what torque is required by the motor. Because the greatest forces are required at the upright and reclined positions, the linkage bar should be in line with the motor shaft at these positions in order to minimize the torque. The shaft of the gear motor is 2.5” from the motor’s base so the center of the cam will need to be at this position vertically. The horizontal position of the motor and the size of the cam are dependent on the desired range of motion of the chair. For the 7” of travel that is to be provided, analysis in Working Model and Visio found the ideal motor shaft position to be 4” from the back of the chair when it is fully upright. The cam size was also determined to be 0.8” in radius. If a circular cam is determined to be too difficult to machine a bar of equal length could be used in place of the cam. The length of the linkage bar was found to be 5”.
Table 4: Torque requirements of the motor
The torques found through static analysis closely matched the values from the Working Model program. The maximum torque in the Working Model simulation was found to be 41.2 in-lb, which occurred as the chair was lowering towards it most reclined position.
Gearmotor
The above analysis found the maximum torque on the motor to be 41.2 in-lb. Gearmotors on the website of Grainger Inc. [2] come in a variety of horsepowers and speeds. A 1/15 HP gearmotor at a comfortable speed of 20 RPM has a full load torque of 150 in-lb and a overhung load rating of 250 pounds. A 1/30 HP gearmotor at 21 RPM has a full load torque of only 50 in-lb. Though the 1/15 HP gearmotor would have 3.6 times the calculated necessary torque, this motor is the ideal choice. The calculated values, though as accurate as possible at this point, will vary with the exact chair purchased and with the exact construction methods used. The high safety factor in for both full load torque and overhung load rating will provide the chair with greater reliability. The selected gearmotor, a Dayton model #1L474, is sold for $269.25 on Grainger’s website. This motor has full load current draw of 6.5 amps. A Dayton model #1L474 motor is provided for free from the Biomedical Engineering stock room. This motor has a speed of 6RPM so an external gear system will be needed to create the necessary speed of approximately 20RPM.