Numerous solutions for gravity compensation have been previously developed in the form of zero-length spring gravity equilibrators [52]. First, the gear deflection according to VDI 2736 (5) and ISO 6336 (4) standards is obtained where the values are calculated in six steps giving the six points of curve in Stress-Strain diagram (see Figure1). A free-body diagram of each link can be drawn as long as the forces and moments sum to zero. Obviously its DOF is not zero. Figure 1.6. endobj 
The main benefit of a parallelogram four-bar linkage is that it simplifies the motion and therefore the design. The inner-supporting mechanical gripper adopts a four-bar linkage mechanism to transmit the supporting force, and the supporting direction is opposite the outer clamping type of these two modes. They can be arranged into a more compact matrix form. The solution can be calculated graphically by choosing an appropriate scale for the length of the vector or using trigonometry. (1.9) needs to be solved.
In the real design, this force vector would be measured from the amount of force it takes to pull the trunk lid downward against the gasket. Types of joints with degrees of freedom. Therefore, the number of actuators and the DOF of the end effector are priorities in analysis and synthesis of a mechanism. What I am going to describe is called a static analysis and it assumes that the mechanism is moving slow enough that you can ignore the dynamic forces. It will be shown in Chapter 2 that Md is different from the actual driving torque transmitted to the driving link. The assembly robot performs various assembly operations and is completed by the end effector. The rack and pinion parallel link type of moving gripper drives the rack and the sector gear through the electromagnetic drive and drives two connecting rods, a claw, and a gripper to form a parallel, Flight Dynamics and System Identification for Modern Feedback Control, Design of a bidirectional energy harvester with a single piezoelectric stack, Mechanical Design of Piezoelectric Energy Harvesters, -fixed have the same shape. In general, the end effector has a specific function, but it can also be designed as a multipurpose structure for a variety of work tasks [26]. The procedural steps of the method are presented subsequently. 155 0 obj Figure2. Extra bodies for the tail surface were not modeled, as the tail has only 4.9% of the mass, moves slowly relative to the flapping wings, and does not create a significant change in the mass distribution. Thus, only J4 is needed. m2r2 and m4r4 are calculated by, To this point, the inertial force is eliminated by m2 and m4. In the previous section, the method for balancing the shaking force was presented, while the shaking moment remained untouched, while taking the four-bar mechanism shown in Fig. As shown in Figure 9.37, Ive added force vectors to the linkage diagram. For all other models deflection is smaller. 27 0 obj Other constraints are placed where the gear has been sliced. Compliant double parallel four-bar mechanism. Link 3 has a general planar motion, thus it is the key in the balancing. 29 0 obj Additionally, limited actuator and pilot bandwidths led to steady models of the tail aerodynamics. Torsion and lateral bending modes in the fuselage are at higher frequencies than used in control. The number of actuators and the DOF of the end effector are two different concepts, which should be treated separately in the kinematic analysis. I always resist the desire to create something from scratch and first search for existing solutions. Applying these to each individual moving link, one has the following. It can be seen from Figure4 that FEM-HE-1 (numerical model with 1 tooth and hyperelastic material behaviour) and FEM-E-1 (numerical model with 1 tooth and linear elastic material behaviour) have a larger deflections if compared to the reference approach. When there is a push input, position limiter B takes effect; it can be treated as the fixed part of the lever mechanism. In addition, each higher pair and lower pair introduce two and one reaction forces, respectively. Figure 9.31 shows how a four-bar linkage with unequal link lengths can create a toggle mechanism similar to the slider crank toggle mechanism. The methods to accomplish this are going to vary by industry so I am going to aim my comments at mechanisms that are lightly loaded and low speed. Berkof (1973) discussed two possible cases of a physical pendulum. %PDF-1.7 % Of course you dont get something for nothing, so the downside of the infinite mechanical advantage is that the range of motion of the output link is small at the toggle position. If the linkage CD is selected to be the end effector, then according to Figure 1.6, the mobility should be zero; however, if BC is selected as the end effector, then it will have one rotational DOF around the z-axis. Several position vectors Si, pi, qi, ri, and ri1 are also involved, which are shown in Fig. This issue will be analyzed in detail in the subsequent chapter and particularly in Chapter 9. Method for mechanism design. It is assumed that the pilot or autopilot directly controls the flapping frequency and orientation of the tail. Instead, the tail mass and inertia was absorbed into the fuselage. The wedge bar rotary mechanical gripper uses a wedge and lever structure to cause a gripping action and clamping force of the gripper to clamp the workpiece. Car trunk lock mechanism with Crank defined. This method plays right into the strength of parametric sketchers that are included in most CAD software. Again a graphical method is the easiest to understand, so I will illustrate using the car trunk lock mechanism from the case study. Modifying the link lengths of the four-bar linkage produces a variety of motions that can be useful. The full effect of downwash from the wings, unsteady aerodynamic effects from the body pitching motion, and flexibility in mechanisms is not currently known. The jaws support the workpiece from the inner hole of the workpiece; most of the three grippers are used to position the inner bore after the tension. The simplified analysis described above is only valid if you enforce the simplifying assumptions with actual design. Two approaches have been taken into account in the numerical analyses: (i) elastic Hooks law approach and (ii) hyperelastic approach. Influence of number of teeth and material models on tooth deflection, Jingshan Zhao, Ning Ma, in Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms, 2014. This describes the motion of the rocker arm and defines its center of rotation (Figure 9.35). 2.11.
In the simplest form, this linkage is composed of four hinge joints connecting four links. In addition to the linear forces, the graphical analysis will also include twisting forces called moments, which are represented by a curved arrow. Numerical model with five teeth. A three-pulley zero-length spring gravity equilibrator can provide perfect gravity balancing of mass, m, and allow a large degree of freedom in the placement of the spring fixed to ground. Both shaking force and shaking moment cause vibration of the machine frame. pi, and qi can be easily obtained from the figure as: Eqs. ">p[R. sj*,T!p}xhkjNOgfyT,jkrA+CSG)3P ;-{.g5F7Iq!\+x)>MhrKGsv2E~M&M );F}..DaC^_}$ %Bbp7$d@p mk!3[cNCU4}N[n vr!!!R /Zi eA X-, Kinematic analysis and synthesis of four-bar mechanisms for straight line coupler curves. The mechanism reaches up and grabs the hook on the trunk lid and pulls it down compressing the trunk lid gasket. It should be pointed out that, if the crank (link 2) rotates at a constant angular speed, then MS on link 2 is zero. Now that you know the applied force, you must go through joint by joint and design for the specified motion and low friction. Step 2 of the process is to use simple rules of sketching to synthesize the rocker arm. While the mechanism will experience some internal loading due to the moment arms developed in the coronal plane, a significant amount of external loading will occur simply from maintaining vertical position against gravitational forces.
Moments are also called couples, because any moment can be replaced in the graphical diagram with a couple, or two, parallel forces. According to the D'Alembert's principle, the equilibrium equations for a moving link i can be represented in a vectorial form as. 3 0 obj Joel C. Perry, Eric T. Wolbrecht, in Wearable Robotics, 2020. According to the moment balance principle in the static situation, the governing equation for the lever mechanism can be determined as: where lbc is the displacement between the two parts, b and c. Considering Eq. The elastic force is released by the wedge rearward movement to release the gripper [26]. The first 3 degrees of freedom describe the position and traditionally are given variable names x, y, and z. I start most mechanism designs by selecting from a short list of classical linkages to see if one of these will solve the problem. Steps to solve with computers are summarized in a flowchart in Fig. application of the four bar mechanism and the gear for a slow motion of the gear rack). Especially if I have space, integrated motor drives can reduce the design time dramatically. A vector represents magnitude and direction which is expressed by the length and angle of the arrow, respectively. (I have assumed I can neglect friction in the joints.) The design of joints is one area where I stick to two basic principles: (i) always attempt to use a lower order of joint whenever possible and (ii) try to purchase joints from off-the-shelf. As for the link BiCi, its DOFs are different from that of the above mechanisms. 6 0 obj The method developed based on the four-bar mechanism, however, can be easily extended to more complicated linkages. 26 0 obj In this actuation scheme, the motion of the other two kinematic chains is still uncertain. For example, if the two actuators are added to the sliders A1 and A2, it can be found that the end effector C1C2C3 and the linkage BiCi can still freely move up and down; but if these two actuators are assigned to Ai and Bi (i=1,2,3), respectively, the end effector C1C2C3 could be completely controlled. According to conventional knowledge, it means that after the two actuations are imposed on the mechanism, they will be able to fully control the entire motion of the whole mechanism. These models can be easily incorporated to increase model fidelity. 12, the compliant double parallel four-bar mechanism can be combined by the proposed linear-motion mechanism, in order to further diminish the parasitic motion. The downwash from the wings onto the tail is assumed negligible due to the placement of the tail between and above the wings. The case study for the car trunk lock mechanism demonstrates the graphical method by synthesizing a car trunk lock mechanism. Figure 1.4. I will discuss robust mechanism design and methods for calculating loads and forces. where Fi and Mi are the resultant force and resultant moment, respectively, on the i-th link. It is generally believed that the calculation result of the DOF equals the number of the actuators. 2020-06-11T10:12:26-07:00 Figure 1.5. A mechanism is a set of parts working together to change an input motion, usually from an electric motor, into a different, more useful output motion. Figure 9.24 shows the more common types of joints and includes the degrees of freedom of each one. Therefore, the mechanism design under a push input is simplified as shown in Fig. The total moment after adding these rotating counter moments becomes. The forces in the joints reflect the degrees of freedom of the joint type. It also attaches sensors for control. Copyright 2022 Elsevier B.V. or its licensors or contributors. 7.4. 2.10(b) are added through gear trains of 1:1 speed ratio. Now lets focus on one of the more exciting parts of mechanical designmechanisms.
where fy,d and fy,b are the y-axis forces of parts d and b, respectively. What remains is to find a rotation point for the third bar of the four-bar link, which we will call the rocker arm (Figure 9.34). The second basic principle is to purchase joints off-the-shelf whenever possible because you are also purchasing a wealth of engineering and design. Figure4. 2.11(b) the condition can be represented as. 154 0 obj Fij=Fji has been applied provided that they are actionreaction force pairs. Figure 9.30. Car trunk lock mechanism with free-body diagrams. 2.9 as an example. In the presented numerical simulations the static load of gear teeth is considered which is based on the assumption that the number of cycles during service life of the gear is very small and the gear is used only for partial rotation (e. g. application of the four bar mechanism and the gear for a slow motion of the gear rack). With these notations and conventions, the free body diagrams (FBD) of all moving links can be drawn as in Fig. 156 0 obj endobj First approach uses Youngs modulus E as shown in Figure3 and Poisson's ratio 0.4. endobj
Structural dynamics in the vehicle dynamics are ignored. Prince 12.5 (www.princexml.com) Now let's look at the shaking moment, which can be represented as (Norton, 2004), where i is the angular acceleration of the link i (i=24) and Ai are the coefficients. The final results of the computational analyses and comparison to the analytical results are presented in section 4. This makes the mechanism an ideal candidate for applying a gravitational compensation method. Thus, the total number of unknowns, including reaction forces and equilibrium torques, in a mechanism is 2nL+nH+f=3n. Figure 9.24. Any point on the rotating link travels in a circular arc. The claw mechanism is equipped with various sensors such as tactile, force, and displacement. The end effector is located at the end of the wrist joint and is used to grab the workpiece directly during assembly. Figure 9.22.
Furthermore, another part of the mechanism, which is a kind of lever mechanism, is shown in Fig. This classical method of mechanism design is shown in Figure 9.22. Two notes should be made regarding these equations. One is the rectangular bar, and the other is the dogbone bar as shown in Fig. The solution for all discrete positions gives the overall result. In the previous section, the method for balancing the shaking force was presented, while the shaking moment remained untouched, while taking the, Robot Systems for Rail Transit Applications, ]. Figure 9.36. Note that the four-bar linkages in the delta printer require ball joints, not hinge joints. This change of direction generates a toggle-type mechanism that can effectively clamp or hold a heavy part in a precise position as shown in Figure 9.27. Figure 9.30 shows how three- and four-bar linkages are combined to create the linkage of a delta printer. Substituted it into formula (1.4), the calculation result F=2 can be obtained. Therefore, I am going to sketch the hook arm extending from the coupler link since I know from experience that this will have that type of motion. The one developed by Berkof (1973) is relatively clear in concept. Depending on the application and structure, end effectors can be divided into mechanical grippers, special tools, and universal hands. Then, the gripper or the robot can have adaptive and intelligent control. For example, as shown in Figure 1.5, it is a special four-bar mechanism [94], whose projection in the z-direction is shown in Figure 1.6. 30 0 obj Figure 9.32 shows the motion of the input and output links; any point on those links is simple circular motion. Obviously, complete balancing of both force and moment is much more complicated than only balancing the shaking force. These two principles help improve the reliability of the joints, which is key because most mechanism failures can be traced back to failure of one of the joints. According to the Gruebler's equation, the number of degrees of freedom (DOF) of a planar mechanism is calculated by. The slider crank has some interesting and very useful attributes. Figure 9.25. endobj 6.9. When opposite links are of equal length, the linkage forms a parallelogram and the linkage enforces parallel motion. The superscripts x and y represent the components of a vector along thex and y directions, respectively. To make MS zero, the following conditions should be met: Combining Eqs. endobj Jared A. Grauer, James E. Any point on the sliding link travels in a straight line. Links and joints of a mechanism. Herder, Energy-Free Systems; Theory, Conception and Design of Statically Balanced Spring Mechanisms (Ph.D. thesis), Delft University of Technology, ISBN 90-370-0192-0 (, Balancing of planar mechanisms and engine dynamics, Both shaking force and shaking moment cause vibration of the machine frame. A four-bar linkage shown in Fig. For a general planar mechanism, f is the number of inputs (driving links) needed. Simple mechanisms can amplify the power of a small electric motor and create useful motions. I like the graphical method for mechanism synthesis. The example I described was a flat, two-dimensional, type of mechanism but the principles can be extended to three dimensions [23]. Mechanisms for simple rotary and linear motion. The principle of choosing a lower level joint is based on my experience that a simple hinge joint can be made to last longer and operate more accurately than a higher order ball joint. If the market is heavy or high-speed machinery, this requires constant and dedicated lubrication which is beyond the scope of this discussion. 1.3. Complex motions such as walking-type motions can be achieved by selecting the proper point on the coupler link along with specific link lengths.
7.2. These can be treated as a parallel four-bar mechanism, and the relationships are governed by: Figure7.6. The first two equations are for shaking-force balancing; the third is the condition for physical pendulum, while the latter two define the moments of inertia required for the balancing. For each discrete position, Eq. If BI is set to be zero, this analysis would be degraded to static analysis. It is obvious there are an infinite number of combinations of link lengths, each creating a unique mechanism, but what is not obvious is that the coupler link of each unique mechanism can unlock an infinite number of motion paths.
The main benefit of a parallelogram four-bar linkage is that it simplifies the motion and therefore the design. The inner-supporting mechanical gripper adopts a four-bar linkage mechanism to transmit the supporting force, and the supporting direction is opposite the outer clamping type of these two modes. They can be arranged into a more compact matrix form. The solution can be calculated graphically by choosing an appropriate scale for the length of the vector or using trigonometry. (1.9) needs to be solved. In the real design, this force vector would be measured from the amount of force it takes to pull the trunk lid downward against the gasket. Types of joints with degrees of freedom. Therefore, the number of actuators and the DOF of the end effector are priorities in analysis and synthesis of a mechanism. What I am going to describe is called a static analysis and it assumes that the mechanism is moving slow enough that you can ignore the dynamic forces. It will be shown in Chapter 2 that Md is different from the actual driving torque transmitted to the driving link. The assembly robot performs various assembly operations and is completed by the end effector. The rack and pinion parallel link type of moving gripper drives the rack and the sector gear through the electromagnetic drive and drives two connecting rods, a claw, and a gripper to form a parallel, Flight Dynamics and System Identification for Modern Feedback Control, Design of a bidirectional energy harvester with a single piezoelectric stack, Mechanical Design of Piezoelectric Energy Harvesters, -fixed have the same shape. In general, the end effector has a specific function, but it can also be designed as a multipurpose structure for a variety of work tasks [26]. The procedural steps of the method are presented subsequently. 155 0 obj Figure2. Extra bodies for the tail surface were not modeled, as the tail has only 4.9% of the mass, moves slowly relative to the flapping wings, and does not create a significant change in the mass distribution. Thus, only J4 is needed. m2r2 and m4r4 are calculated by, To this point, the inertial force is eliminated by m2 and m4. In the previous section, the method for balancing the shaking force was presented, while the shaking moment remained untouched, while taking the four-bar mechanism shown in Fig. As shown in Figure 9.37, Ive added force vectors to the linkage diagram. For all other models deflection is smaller. 27 0 obj Other constraints are placed where the gear has been sliced. Compliant double parallel four-bar mechanism. Link 3 has a general planar motion, thus it is the key in the balancing. 29 0 obj Additionally, limited actuator and pilot bandwidths led to steady models of the tail aerodynamics. Torsion and lateral bending modes in the fuselage are at higher frequencies than used in control. The number of actuators and the DOF of the end effector are two different concepts, which should be treated separately in the kinematic analysis. I always resist the desire to create something from scratch and first search for existing solutions. Applying these to each individual moving link, one has the following. It can be seen from Figure4 that FEM-HE-1 (numerical model with 1 tooth and hyperelastic material behaviour) and FEM-E-1 (numerical model with 1 tooth and linear elastic material behaviour) have a larger deflections if compared to the reference approach. When there is a push input, position limiter B takes effect; it can be treated as the fixed part of the lever mechanism. In addition, each higher pair and lower pair introduce two and one reaction forces, respectively. Figure 9.31 shows how a four-bar linkage with unequal link lengths can create a toggle mechanism similar to the slider crank toggle mechanism. The methods to accomplish this are going to vary by industry so I am going to aim my comments at mechanisms that are lightly loaded and low speed. Berkof (1973) discussed two possible cases of a physical pendulum. %PDF-1.7 % Of course you dont get something for nothing, so the downside of the infinite mechanical advantage is that the range of motion of the output link is small at the toggle position. If the linkage CD is selected to be the end effector, then according to Figure 1.6, the mobility should be zero; however, if BC is selected as the end effector, then it will have one rotational DOF around the z-axis. Several position vectors Si, pi, qi, ri, and ri1 are also involved, which are shown in Fig. This issue will be analyzed in detail in the subsequent chapter and particularly in Chapter 9. Method for mechanism design. It is assumed that the pilot or autopilot directly controls the flapping frequency and orientation of the tail. Instead, the tail mass and inertia was absorbed into the fuselage. The wedge bar rotary mechanical gripper uses a wedge and lever structure to cause a gripping action and clamping force of the gripper to clamp the workpiece. Car trunk lock mechanism with Crank defined. This method plays right into the strength of parametric sketchers that are included in most CAD software. Again a graphical method is the easiest to understand, so I will illustrate using the car trunk lock mechanism from the case study. Modifying the link lengths of the four-bar linkage produces a variety of motions that can be useful. The full effect of downwash from the wings, unsteady aerodynamic effects from the body pitching motion, and flexibility in mechanisms is not currently known. The jaws support the workpiece from the inner hole of the workpiece; most of the three grippers are used to position the inner bore after the tension. The simplified analysis described above is only valid if you enforce the simplifying assumptions with actual design. Two approaches have been taken into account in the numerical analyses: (i) elastic Hooks law approach and (ii) hyperelastic approach. Influence of number of teeth and material models on tooth deflection, Jingshan Zhao, Ning Ma, in Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms, 2014. This describes the motion of the rocker arm and defines its center of rotation (Figure 9.35). 2.11.
In the simplest form, this linkage is composed of four hinge joints connecting four links. In addition to the linear forces, the graphical analysis will also include twisting forces called moments, which are represented by a curved arrow. Numerical model with five teeth. A three-pulley zero-length spring gravity equilibrator can provide perfect gravity balancing of mass, m, and allow a large degree of freedom in the placement of the spring fixed to ground. Both shaking force and shaking moment cause vibration of the machine frame. pi, and qi can be easily obtained from the figure as: Eqs. ">p[R. sj*,T!p}xhkjNOgfyT,jkrA+CSG)3P ;-{.g5F7Iq!\+x)>MhrKGsv2E~M&M );F}..DaC^_}$ %Bbp7$d@p mk!3[cNCU4}N[n vr!!!R /Zi eA X-, Kinematic analysis and synthesis of four-bar mechanisms for straight line coupler curves. The mechanism reaches up and grabs the hook on the trunk lid and pulls it down compressing the trunk lid gasket. It should be pointed out that, if the crank (link 2) rotates at a constant angular speed, then MS on link 2 is zero. Now that you know the applied force, you must go through joint by joint and design for the specified motion and low friction. Step 2 of the process is to use simple rules of sketching to synthesize the rocker arm. While the mechanism will experience some internal loading due to the moment arms developed in the coronal plane, a significant amount of external loading will occur simply from maintaining vertical position against gravitational forces.
Moments are also called couples, because any moment can be replaced in the graphical diagram with a couple, or two, parallel forces. According to the D'Alembert's principle, the equilibrium equations for a moving link i can be represented in a vectorial form as. 3 0 obj Joel C. Perry, Eric T. Wolbrecht, in Wearable Robotics, 2020. According to the moment balance principle in the static situation, the governing equation for the lever mechanism can be determined as: where lbc is the displacement between the two parts, b and c. Considering Eq. The elastic force is released by the wedge rearward movement to release the gripper [26]. The first 3 degrees of freedom describe the position and traditionally are given variable names x, y, and z. I start most mechanism designs by selecting from a short list of classical linkages to see if one of these will solve the problem. Steps to solve with computers are summarized in a flowchart in Fig. application of the four bar mechanism and the gear for a slow motion of the gear rack). Especially if I have space, integrated motor drives can reduce the design time dramatically. A vector represents magnitude and direction which is expressed by the length and angle of the arrow, respectively. (I have assumed I can neglect friction in the joints.) The design of joints is one area where I stick to two basic principles: (i) always attempt to use a lower order of joint whenever possible and (ii) try to purchase joints from off-the-shelf. As for the link BiCi, its DOFs are different from that of the above mechanisms. 6 0 obj The method developed based on the four-bar mechanism, however, can be easily extended to more complicated linkages. 26 0 obj In this actuation scheme, the motion of the other two kinematic chains is still uncertain. For example, if the two actuators are added to the sliders A1 and A2, it can be found that the end effector C1C2C3 and the linkage BiCi can still freely move up and down; but if these two actuators are assigned to Ai and Bi (i=1,2,3), respectively, the end effector C1C2C3 could be completely controlled. According to conventional knowledge, it means that after the two actuations are imposed on the mechanism, they will be able to fully control the entire motion of the whole mechanism. These models can be easily incorporated to increase model fidelity. 12, the compliant double parallel four-bar mechanism can be combined by the proposed linear-motion mechanism, in order to further diminish the parasitic motion. The downwash from the wings onto the tail is assumed negligible due to the placement of the tail between and above the wings. The case study for the car trunk lock mechanism demonstrates the graphical method by synthesizing a car trunk lock mechanism. Figure 1.4. I will discuss robust mechanism design and methods for calculating loads and forces. where Fi and Mi are the resultant force and resultant moment, respectively, on the i-th link. It is generally believed that the calculation result of the DOF equals the number of the actuators. 2020-06-11T10:12:26-07:00 Figure 1.5. A mechanism is a set of parts working together to change an input motion, usually from an electric motor, into a different, more useful output motion. Figure 9.24 shows the more common types of joints and includes the degrees of freedom of each one. Therefore, the mechanism design under a push input is simplified as shown in Fig. The total moment after adding these rotating counter moments becomes. The forces in the joints reflect the degrees of freedom of the joint type. It also attaches sensors for control. Copyright 2022 Elsevier B.V. or its licensors or contributors. 7.4. 2.10(b) are added through gear trains of 1:1 speed ratio. Now lets focus on one of the more exciting parts of mechanical designmechanisms.
where fy,d and fy,b are the y-axis forces of parts d and b, respectively. What remains is to find a rotation point for the third bar of the four-bar link, which we will call the rocker arm (Figure 9.34). The second basic principle is to purchase joints off-the-shelf whenever possible because you are also purchasing a wealth of engineering and design. Figure4. 2.11(b) the condition can be represented as. 154 0 obj Fij=Fji has been applied provided that they are actionreaction force pairs. Figure 9.30. Car trunk lock mechanism with free-body diagrams. 2.9 as an example. In the presented numerical simulations the static load of gear teeth is considered which is based on the assumption that the number of cycles during service life of the gear is very small and the gear is used only for partial rotation (e. g. application of the four bar mechanism and the gear for a slow motion of the gear rack). With these notations and conventions, the free body diagrams (FBD) of all moving links can be drawn as in Fig. 156 0 obj endobj First approach uses Youngs modulus E as shown in Figure3 and Poisson's ratio 0.4. endobj
Structural dynamics in the vehicle dynamics are ignored. Prince 12.5 (www.princexml.com) Now let's look at the shaking moment, which can be represented as (Norton, 2004), where i is the angular acceleration of the link i (i=24) and Ai are the coefficients. The final results of the computational analyses and comparison to the analytical results are presented in section 4. This makes the mechanism an ideal candidate for applying a gravitational compensation method. Thus, the total number of unknowns, including reaction forces and equilibrium torques, in a mechanism is 2nL+nH+f=3n. Figure 9.24. Any point on the rotating link travels in a circular arc. The claw mechanism is equipped with various sensors such as tactile, force, and displacement. The end effector is located at the end of the wrist joint and is used to grab the workpiece directly during assembly. Figure 9.22.
Furthermore, another part of the mechanism, which is a kind of lever mechanism, is shown in Fig. This classical method of mechanism design is shown in Figure 9.22. Two notes should be made regarding these equations. One is the rectangular bar, and the other is the dogbone bar as shown in Fig. The solution for all discrete positions gives the overall result. In the previous section, the method for balancing the shaking force was presented, while the shaking moment remained untouched, while taking the, Robot Systems for Rail Transit Applications, ]. Figure 9.36. Note that the four-bar linkages in the delta printer require ball joints, not hinge joints. This change of direction generates a toggle-type mechanism that can effectively clamp or hold a heavy part in a precise position as shown in Figure 9.27. Figure 9.30 shows how three- and four-bar linkages are combined to create the linkage of a delta printer. Substituted it into formula (1.4), the calculation result F=2 can be obtained. Therefore, I am going to sketch the hook arm extending from the coupler link since I know from experience that this will have that type of motion. The one developed by Berkof (1973) is relatively clear in concept. Depending on the application and structure, end effectors can be divided into mechanical grippers, special tools, and universal hands. Then, the gripper or the robot can have adaptive and intelligent control. For example, as shown in Figure 1.5, it is a special four-bar mechanism [94], whose projection in the z-direction is shown in Figure 1.6. 30 0 obj Figure 9.32 shows the motion of the input and output links; any point on those links is simple circular motion. Obviously, complete balancing of both force and moment is much more complicated than only balancing the shaking force. These two principles help improve the reliability of the joints, which is key because most mechanism failures can be traced back to failure of one of the joints. According to the Gruebler's equation, the number of degrees of freedom (DOF) of a planar mechanism is calculated by. The slider crank has some interesting and very useful attributes. Figure 9.25. endobj 6.9. When opposite links are of equal length, the linkage forms a parallelogram and the linkage enforces parallel motion. The superscripts x and y represent the components of a vector along thex and y directions, respectively. To make MS zero, the following conditions should be met: Combining Eqs. endobj Jared A. Grauer, James E. Any point on the sliding link travels in a straight line. Links and joints of a mechanism. Herder, Energy-Free Systems; Theory, Conception and Design of Statically Balanced Spring Mechanisms (Ph.D. thesis), Delft University of Technology, ISBN 90-370-0192-0 (, Balancing of planar mechanisms and engine dynamics, Both shaking force and shaking moment cause vibration of the machine frame. A four-bar linkage shown in Fig. For a general planar mechanism, f is the number of inputs (driving links) needed. Simple mechanisms can amplify the power of a small electric motor and create useful motions. I like the graphical method for mechanism synthesis. The example I described was a flat, two-dimensional, type of mechanism but the principles can be extended to three dimensions [23]. Mechanisms for simple rotary and linear motion. The principle of choosing a lower level joint is based on my experience that a simple hinge joint can be made to last longer and operate more accurately than a higher order ball joint. If the market is heavy or high-speed machinery, this requires constant and dedicated lubrication which is beyond the scope of this discussion. 1.3. Complex motions such as walking-type motions can be achieved by selecting the proper point on the coupler link along with specific link lengths.
7.2. These can be treated as a parallel four-bar mechanism, and the relationships are governed by: Figure7.6. The first two equations are for shaking-force balancing; the third is the condition for physical pendulum, while the latter two define the moments of inertia required for the balancing. For each discrete position, Eq. If BI is set to be zero, this analysis would be degraded to static analysis. It is obvious there are an infinite number of combinations of link lengths, each creating a unique mechanism, but what is not obvious is that the coupler link of each unique mechanism can unlock an infinite number of motion paths.