IROS2019国际学术会议论文集 0541

1 Abstract In this paper we propose a new compact variable gravity compensation mechanism CVGC The CVGC can be used to generate gravity compensation torque by using the cam and lever mechanism and can also amplify the target gravity compensation torque by varying the pivot point of the lever The feature of variable gravity compensation is very useful to the mobile platform which needs to handle unstandardized tasks with a high variation of the workpiece weight The proposed CVGC has many advantages Most importantly it is designed as a compact independent one piece structure and is lightweight meaning it can easily be used as a mobile platform with a simple modification The CVGC can also have a full range of compensation angle 360 so it does not restrict any of the original workspaces of the target platform when it is installed First the mechanism concept and details are explained Next the mechanics of the prototype for force analysis are presented Based on these mechanics and cam theory the methodology of the cam profile design is presented Finally the performance of variable gravity compensation is verified through experiments that compare the designed and measured gravity compensation torque The verification test shows adequate performance as we had hoped which shows potential for the development of the CVGC I INTRODUCTION For more than a century gravity compensation mechanisms have been developed to reduce actuator capacity and improve the energy efficiency of the system by partial or full compensation of gravitational torque 1 The mechanism has been applied to industrial manipulator robots for decades to reduce the maintenance cost of electrical power consumption In recent years the applications have been expanded to the mobile platform e g exoskeleton robots mobile robots to reduce the system weight and size by improving the energy efficiency of the actuators 2 10 Several types of gravity compensation mechanisms have been proposed with satisfactory results Deepak et al Lenzo et al and Lin et al studied the optimal arrangement of multiple springs for a complete static balance of connectors of a general structure 11 13 Lin et al and This work has supported by the National Research Foundation of Korea NRF grant funded by the Korea government MSIT NRF 2018R1C1B5043746 for the prototype manufacturing cost This work has also supported by Samsung Research Funding email giuklee cau ac kr Baradat et al studied gravity compensation mechanisms for use in a general industrial manipulator using additional structures and springs 14 15 The introduced studies of gravity compensators have been effectively applied to industrial manipulator robots performing with a constant payload in standardized tasks However because the gravitational compensation torque is constant these studies are limited in their application to nonstandardized tasks where the payload changes frequently In particular the mobile platforms need to handle many types of nonstandardized tasks with high variations of workpiece weight Because of these different operating conditions of the mobile platform it is difficult to compensate for the gravitational torque efficiently Moreover an improper gravity compensation torque can cause side effects that add an overload to the system In several studies the authors have attempted to design a new gravity compensation mechanism with the ability to change the gravity compensation torque to mitigate the limited application to mobile systems Takesue et al s presented mechanism used two types of linear springs This dealt with variable gravity compensation by changing its equilibrium position 16 Briot et al presented an adaptive compensation system that could change compensation torque without outside energy 17 These gravity compensation mechanisms showed decent performance to change the gravity compensation capacity however they required various types of additional structures As the structure becomes more complex the size and weight of the mechanisms increase making it more challenging to implement on mobile platforms To overcome the abovementioned limitation several authors have attempted to reduce the size and weight for the feature of variable gravity compensation Yang et al presented the mechanism with dual customized springs Changing the preload of the tension spring can vary the compensation torque Altenburger et al presented a mechanism consisting of a parallelogram and four bar linkage By changing the shape of the four bar linkage variable gravity compensation can be achieved Both research teams proposed a small variable gravity compensation mechanism which performed successfully However due to their small operating range of rotation the workspace of the system can be constrained than it was originally 18 19 To overcome the shortcomings of the large size heavy weight and limited operating range of the rotation angle in Design of Compact Variable Gravity Compensator CVGC Based on Cam and Variable Pivot of a Lever Mechanism Jehyeok Kim Junyoung Moon Jongwon Kim and Giuk Lee Member IEEE 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE3583 previous studies we propose a new gravity compensation mechanism called a compact variable gravity compensation CVGC mechanism The CVGC is much lighter and smaller than the previous mechanisms because it consists of a simple structure with a small size cam and compact lever mechanism with a variable pivot point The CVGC is also designed as an independent one piece structure that can be easily installed on the mobile platform with simple modifications Moreover the CVGC has the potential to compensate for a full range of motion which could not be achieved with certain previous gravity compensation mechanisms The paper is organized as follows Section II explains the mechanism concept details of the CVGC and the methodology of the cam profile design Section III describes a prototype manufacturing and the experiments and results to verify the performance of the CVGC Finally conclusions are presented in section IV II MECHANICAL DESIGN A CVGC mechanism concepts The CVGC has two mechanisms as shown in Figure 1 that achieve the primary functional goals of 1 generating a referential compensation torque profile and 2 varying the amplitude of reference compensation torque The mechanism for realizing the first functional goal of generating the target compensating torque consisted of a cam and lever mechanism as shown in Figure 1 a The cam mechanism was connected to the payload and rotated as the payload rotated The rotation of the cam compressed the spring by the lever rotating about the pivot point and generating the restoring force The generated force was transmitted back to the cam via the lever and generated a gravity compensation torque on the cam according to the moment arm of the force which was determined by the pressure angle of the cam profile Thus any target gravity compensation torque could be generated using an appropriate gravity profile The mechanism for realizing the second functional goal of varying the amplitude of the target compensation torque was based on the variable pivot position of the lever as shown in Figure 1 b When the position of the pivot was varied the distance between the pivot and the cam follower 1 and the distance between the pivot and the spring follower 2 were changed simultaneously Because these distances determined the amplitude ratio of the lever force the amplitude of gravity compensation torque could be varied by changing the pivot position Fundamentally these two mechanisms are highly useful for miniaturization of CVGC Through the lever mechanism the CVGC can overcome the limitation of spring force due to its compact size by amplifying the force used to generate the compensating torque Furthermore the movement of the pivot point changes the compression length of the spring and the force amplification ratio of the lever simultaneously so that the force of the cam follower can be significantly changed by a short stroke of the pivot These advantages minimize the required size of the mechanism structure for the target specification and enable the design of a CVGC B Detailed mechanism of CVGC The detailed mechanisms to realize the two mechanism concepts are shown in Figure 2 a To implements the first Fig 1 Schematic of CVGC mechanism A position of pivot determines an amplification of spring force a High compensation torque by high pivot position 1 2 Variable pivot Cam Line of variable pivot position Guide Follower a b c d Spring Cam Spring follower Screw Cam follower Lever Pivot Fig 2 Detailed mechanism of CVGC to achieve two primary functional goals a and b show the means of generating a target compensation torque profile c and d show how the CVGC varies the amplitude of target compensation torque a Cam rotation angle is 0 b Cam rotation angle is 180 c Low pivot position d High pivot position 1 2 3584 mechanism concept we used a cam with a cam follower moving on the surface of the cam and a spring follower transmitting the movement of the lever to the spring The lever is in contact with the cam follower and the spring follower The movement of the cam follower by the rotation of the cam causes the rotation of the lever and the movement of the spring The shape of the lever was designed as the angled line for the compact design which differed from the straight line in the mechanism concept Although the shape of the lever was different the function of the lever amplifying the force based on moment equilibrium at the pivot axis was not affected Note that the amplification ratio of the angled lever was calculated by using the length of l1 and l2 in Figure 3 The lead screw mechanism was implemented to change the pivot position Figure 2 shows how we designed the detailed mechanism of CVGC to achieve the two primary functional goals explained in the previous section Figures 2 a and b show the means of generating a target compensation torque profile by using the cam and lever mechanism Figures 2 c and d show that the feature can adjust the pivot point position to amplify the gravity compensation torque profile The schematic of the CVGC for the force analysis is shown in Figure 3 where the cam rotation angle lever shape angle spring guide angle and the radius of cam at that moment are and respectively If the values of these parameters are given the values of other angles and in the mechanism schematic can be calculated according to geometric relationships In this condition the force acting on the spring follower by the compression spring is calculated by equation 1 1 where k is the spring coefficient of the compression spring Because the direction vector of the force acting on the lever by the spring follower is perpendicular to the lever the static force as determined by the force equilibrium at the spring follower is calculated by equation 2 2 was transmitted to the cam follower by a lever that could rotate around the pivot axis The force acting on the cam follower by the lever can be calculated by moment equilibrium 2 1 3 where l1 and l2 are the distance between the pivot and cam follower Because the spring force is amplified to formulate the force at the cam follower the amplification ratio is calculated by 3 2 1 4 Assuming the pressure angle of the cam profile at the cam rotation angle the force acting on the cam by the cam follower can be determined by the force equilibrium at said follower Fig 4 Design process and result of the cam profile a Algorithm of cam profile design b Cam profile extracted by algorithm for CVGC Initial condition cam angle 1 1 Desired torque profile sine shape for gravity compensation Pressure angle at an 1 Calculation of 1 an i 180 NO i i 1 Cam profile for desired torque profile YES i 1 a b Fig 3 Schematic with parameters representation of the CVGC prototype 2 1 3585 5 where can be calculated by 3 The moment arm of the above force about the cam axis is determined by cam geometry as follows in 6 And the resultant compensation torque at cam can be calculated by multiplication of 5 and 6 an 7 As can be seen from 7 the compensation torque of the mechanism is determined by the cam profile including cam radius and pressure angle C Methodology of cam profile design The required torque profile for gravity compensation is in the shape of a sine graph To produce the referential gravity compensation torque it is necessary to determine the relationship between cam radius and pressure angle These two items are dependent on each other Therefore when the cam radius and pressure angle are at a certain cam angle the next radius at an infinitesimally increased cam angle is determined by 8 1 an 8 The cam profile that can generate the desired torque diagram is derived from the algorithm explained in Figure 3 The initial value of the cam radius is decided based on the size restriction of the mechanism In the case of the pressure angle it must be zero as the initial value This is because compensation torque at zero cam angle must be zero even though force acting on the cam is present Based on these initial values the algorithm can produce the cam profile through an iterative process This process consists of calculating the pressure angle at a certain cam angle i and calculating cam radius at the next angle i 1 In this study the cam profile was lowered by one degree increments the results are shown in Figure 3 III EVALUATION A Prototype manufacturing The CVGC prototype was manufactured as shown in Figure 5 Because of the compact independent one piece design it did not require additional structures for installation The weight and size of the prototype was 1 5 kg and 110 70 diameter height The prototype was designed to have a range of compensation torque of 1 3 Nm to 1 9 Nm By changing the position of pivot by 12 mm the target performance was achieved To move the pivoted position a simple screw mechanism was used Many combinations of mechanism parameters exist for desired performance Through a repetitive design process we determined proper values of parameters that make compact design possible without any intervention Therefore we used an angled shape for the lever instead of a straight shape In addition we used the compressive irregular cross section spring which has a higher spring coefficient than a general spring SWF14 80 MISUIMI Japan to reduce the length of the compression spring Because this mechanism basically uses the concept of amplification of spring compression force with a lever mechanism it generates high reaction force on the contacting surfaces between the mechanical components In addition high forces can irrefutable create friction To minimize the effect of the friction on the gravity compensation torque we implemented bearings on the contacting surfaces In particular we used shell type needle roller bearings which have eight to nine times higher allowable static load than a normal ball bearing with the same scale of size At the cam follower axis we used two types of bearings For lever and cam contact we used a needle bearing HK0608 JTEKT KOYO Japan Moreover for the supporting cam follower axis we used a needle bearing HK0709 JTEKT KOYO Japan In the case of a spring follower we used a small ball bearing B678ZZ MISUMI Japan instead of a needle bearing because of the relatively low value of the force Fig 5 The prototype of CVGC mechanism a Prototype with cover b Prototype without cover to shows components 3586 B Measurement of gravity compensation torque As shown in Figure 6 we measured the static torque generated by the CVGC prototype to validate the performance of gravity compensation During the measuring experiment the torque at the cam axis was measured by the torque sensor CNF 500KC CAS Korea when the cam axis was fixed to the sensor and the stator frame was rotated by linking it to a certain angle The testbed has a fixing frame bar to hold the angle of the link of CVGC As shown in Figure 6 b the measurements of the static torque were conducted with 15 degree intervals for 180 degrees with one pivot position We repeated the same procedure of measurements at four different pivot positions with the same interval length 4 mm to evaluate the different gravity compensation profiles according to the change of pivot point The measurement results are shown in Figure 7 The root mean square RMS error between designed and measured compensation torque is 0 3 Nm Comparing the graphs of measured and design values reveals that the maximum value and tendency per pivot position are similar but the measured data are shifted to the right in the x axis direction After calibrating the measured data by considering this tendency the RMS error between the maximum compensation torque value that was designed and measured was 0 07 Nm The measured torque profiles were shifted to the right by 12 degrees on average The exact cause of the shifting requires much analysis but we assume that the error was mainly due to the different sizes of the mechanical components of the ideal geometric model and actual prototype Particularly the bearing radii of the cam follower and spring followers were not considered for the ideal geometric model Because of this the contact position between the lever and follower changed causing the shifting IV CONCLUSION In this paper we proposed a CVGC mechanism using a cam and lever with variable pivot points The mechanical concepts of the primary functions were presented and the detailed mechanism was designed based on the derived equations Finally the prototype was manufactured and we evaluated its performance in generating the gravity compensation torque and varying the gravity compensation torque This mechanism has several advantages Most importantly the variable gravity compensation mechanism is designed as a unit type that is compact and lightweight Therefore this Fig 7 Designed and measure