23. Assembly Mechanics of Manipulation
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1 23. Assembly Mechanics of Manipulation Matt Mason Carnegie Mellon Lecture 23. Mechanics of Manipulation p.1
2 Lecture 23. Assembly. Chapter 1 Manipulation Case 1: Manipulation by a human Case 2: An automated assembly system Issues in manipulation A taxonomy of manipulation techniques Bibliographic notes 8 Exercises 8 Chapter 2 Kinematics Preliminaries Planar kinematics Spherical kinematics Spatial kinematics Kinematic constraint Kinematic mechanisms Bibliographic notes 36 Exercises 37 Chapter 3 Kinematic Representation Representation of spatial rotations Representation of spatial displacements Kinematic constraints Bibliographic notes 72 Exercises 72 Chapter 4 Kinematic Manipulation Path planning Path planning for nonholonomic systems Kinematic models of contact Bibliographic notes 88 Exercises 88 Chapter 5 Rigid Body Statics Forces acting on rigid bodies Polyhedral convex cones Contact wrenches and wrench cones Cones in velocity twist space The oriented plane Instantaneous centers and Reuleaux's method Line of force; moment labeling Force dual Summary Bibliographic notes 117 Exercises 118 Chapter 6 Friction Coulomb's Law Single degree-of-freedom problems Planar single contact problems Graphical representation of friction cones Static equilibrium problems Planar sliding Bibliographic notes 139 Exercises 139 Chapter 7 Quasistatic Manipulation Grasping and fixturing Pushing Stable pushing Parts orienting Assembly Bibliographic notes 173 Exercises 175 Chapter 8 Dynamics Newton's laws A particle in three dimensions Moment of force; moment of momentum Dynamics of a system of particles Rigid body dynamics The angular inertia matrix Motion of a freely rotating body Planar single contact problems Graphical methods for the plane Planar multiple-contact problems Bibliographic notes 207 Exercises 208 Chapter 9 Impact A particle Rigid body impact Bibliographic notes 223 Exercises 223 Chapter 10 Dynamic Manipulation Quasidynamic manipulation Briefly dynamic manipulation Continuously dynamic manipulation Bibliographic notes 232 Exercises 235 Appendix A Infinity 237 Lecture 23. Mechanics of Manipulation p.2
3 Outline. Role of assembly Assembly sequence planning Jamming and wedging Compliance Lecture 23. Mechanics of Manipulation p.3
4 Role of assembly in manufacturing Most assembly still manual? Assembly automation has a big impact. Example: SONY Smart cell High volume production uses more specialized machinery. Low volume production is usually manual. Lecture 23. Mechanics of Manipulation p.4
5 Role of assembly, more generally Assembly is an application of manipulation. It is also a fundamental manipulation technique. Consider Smart cell again: 1. Part is oriented in APOS machine. (By assembling it with pallet nests!) 2. Part is grasped by SCARA gripper. (Another assembly.) 3. Part is placed in product. (Assembly again.) 4. Part is released. (Not assembly! Disassembly.) Even placing an object on a table is an assembly. If assembly is defined to be bringing one shape into a desired configuration relative to another shape, then it is obvious that assembly pervades manipulation. Lecture 23. Mechanics of Manipulation p.5
6 Issues in assembly Assembly sequence. What order to put things together? Local constraint analysis. What motions to join two objects? Path planning and grasp planning. Finding a free path. Gripper and fixture design. Being able to apply the desired forces without interfering with the assembly. Stable subassembly. Partial assemblies must be stable. Assemblability. Even if path exists, parts might be virtually impossible to assemble, due to jamming. Tolerances. All issues must also address variations in shape. Design for assembly. Product design must be integrated with automation design. Lecture 23. Mechanics of Manipulation p.6
7 Assembly sequence Assume assembly. two-handed Look at all possible partitions of the parts. Result is an and/or tree. Every subtree with one and-arc per node is a possible assembly. Lecture 23. Mechanics of Manipulation p.7
8 Local constraint analysis To decide if an assembly motion exists, 1. Reverse time, consider disassembly problem. 2. Look at contact constraints, identify all motion freedoms. 3. First order form analysis often is sufficient. Remember the refrigerator problem? Lecture 23. Mechanics of Manipulation p.8
9 Jamming and wedging One of the earliest papers on the mechanics of manipulation was by Simunovic, in 1974, studying assembly of peg in hole. This was part of a larger project studying manufacturing issues at the Draper Labs, supervised by Nevins and Whitney. Study of several assemblies showed that just a few operations dominate manufacturing. Assembly, joining, etc. Also, just a few directions of motion dominate all assemblies. Mostly vertical. Simunovic defined jamming and wedging: Jamming. An assembly force in equilibrium with the contact forces. Wedging. A configuration such that every possibly force is in equilibrium with the contact forces. I.e. force closure. Lecture 23. Mechanics of Manipulation p.9
10 Jamming and wedging P Wedged Jammed Simunovic s analysis of wedging anticipated Nguyen s approach to planar force closure. Simunovic s analysis of jamming anticipated the moment labeling method. Jamming may occur if the applied force makes positive moment at P. Lecture 23. Mechanics of Manipulation p.10
11 Analysis of wedging Lecture 23. Mechanics of Manipulation p.11
12 Analysis of jamming Lecture 23. Mechanics of Manipulation p.12
13 Compliance Compliance elements rubber/steel sandwiches stiff in compression soft in sheer Compliance center Active force control is an option. Remote Center Compliance is a passive mechanism. Compliance Center: behaves like decoupled translational and rotational springs. Put compliance center at tip of peg or at lip of hole. Lecture 23. Mechanics of Manipulation p.13
14 Next: Newtonian dynamics. Chapter 1 Manipulation Case 1: Manipulation by a human Case 2: An automated assembly system Issues in manipulation A taxonomy of manipulation techniques Bibliographic notes 8 Exercises 8 Chapter 2 Kinematics Preliminaries Planar kinematics Spherical kinematics Spatial kinematics Kinematic constraint Kinematic mechanisms Bibliographic notes 36 Exercises 37 Chapter 3 Kinematic Representation Representation of spatial rotations Representation of spatial displacements Kinematic constraints Bibliographic notes 72 Exercises 72 Chapter 4 Kinematic Manipulation Path planning Path planning for nonholonomic systems Kinematic models of contact Bibliographic notes 88 Exercises 88 Chapter 5 Rigid Body Statics Forces acting on rigid bodies Polyhedral convex cones Contact wrenches and wrench cones Cones in velocity twist space The oriented plane Instantaneous centers and Reuleaux's method Line of force; moment labeling Force dual Summary Bibliographic notes 117 Exercises 118 Chapter 6 Friction Coulomb's Law Single degree-of-freedom problems Planar single contact problems Graphical representation of friction cones Static equilibrium problems Planar sliding Bibliographic notes 139 Exercises 139 Chapter 7 Quasistatic Manipulation Grasping and fixturing Pushing Stable pushing Parts orienting Assembly Bibliographic notes 173 Exercises 175 Chapter 8 Dynamics Newton's laws A particle in three dimensions Moment of force; moment of momentum Dynamics of a system of particles Rigid body dynamics The angular inertia matrix Motion of a freely rotating body Planar single contact problems Graphical methods for the plane Planar multiple-contact problems Bibliographic notes 207 Exercises 208 Chapter 9 Impact A particle Rigid body impact Bibliographic notes 223 Exercises 223 Chapter 10 Dynamic Manipulation Quasidynamic manipulation Briefly dynamic manipulation Continuously dynamic manipulation Bibliographic notes 232 Exercises 235 Appendix A Infinity 237 Lecture 23. Mechanics of Manipulation p.14
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