kinematic chains - 2026 ACF Regionals

Question

The number of degrees of freedom of one of these systems is related to the number of joints by the mobility formula. For 10 points each:

[10h] Name these idealized systems consisting of rigid bodies coupled together by joints.

ANSWER: kinematic chains [or linkages; prompt on mechanisms; prompt on chains]

[10m] If several of these statements for a kinematic chain are redundant, a kinematic chain that the mobility formula predicts to have zero degrees of freedom can still move. Joints are typically modelled as a holonomic one of these statements.

ANSWER: constraints [accept holonomic constraints; accept overconstrained systems or mechanisms]

[10e] Kinematic chains are commonly used to model the manipulators of these machines, which interact with their environment using an end-effector. These autonomous machines are capable of performing complex tasks.

ANSWER: robots [accept robotic manipulators]

<GC, Physics>

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Summary


California (North)	Main Site	Y	3	16.67	100%	67%	0%
Canada	Main Site	Y	1	20.00	100%	100%	0%
Florida	Main Site	Y	2	10.00	100%	0%	0%
Lower Mid-Atlantic	Main Site	Y	9	10.00	78%	22%	0%
Midwest	Main Site	Y	9	11.11	78%	22%	11%
Northeast	Main Site	Y	6	15.00	67%	50%	33%
Overflow	Main Site	Y	4	15.00	100%	50%	0%
South Central	Main Site	Y	2	15.00	100%	50%	0%
Southeast	Main Site	Y	7	8.57	57%	14%	14%
UK	Main Site	Y	6	11.67	83%	33%	0%
Upper Mid-Atlantic	Main Site	Y	9	12.22	89%	33%	0%
Upstate NY	Main Site	Y	4	12.50	100%	25%	0%

Data


Berkeley A	Berkeley D	0	10	10	20
Berkeley B	Stanford B	0	0	10	10
Berkeley C	Stanford A	0	10	10	20
McGill A	UBC B	0	10	10	20
Central Florida C	Central Florida B	0	0	10	10
Central Florida A	Florida C	0	0	10	10
Duke	William and Mary	0	0	0	0
Liberty C	James Madison A	0	0	10	10
South Carolina A	Liberty A	0	0	10	10
James Madison B	Liberty B	0	0	10	10
North Carolina B	NC State B	0	0	10	10
North Carolina C	NC State A	0	0	10	10
VCU	South Carolina B	0	0	10	10
Virginia Tech A	North Carolina A	0	10	10	20
Virginia Tech B	Virginia	0	10	0	10
Notre Dame A	Chicago B	0	0	10	10
Chicago C	Illinois B	0	0	10	10
Purdue B	Chicago D	0	0	10	10
Notre Dame B	Chicago E	0	0	10	10
Illinois A	Indiana A	10	0	0	10
Illinois C	Northwestern B	0	10	10	20
Indiana B	Northwestern D	0	0	10	10
Northwestern C	Indiana C	0	0	0	0
Chicago A	Purdue A	0	10	10	20
Brandeis B	Bowdoin A	0	0	0	0
Brown	Bowdoin B	0	10	0	10
MIT	Brandeis A	10	10	10	30
Yale	Harvard B	0	10	10	20
Carleton College	Washington B	0	0	10	10
Iowa State	Claremont	0	10	10	20
Georgia Tech A	Minnesota A	0	10	10	20
Missouri A	Washington A	0	0	10	10
Texas A	Murray State A	0	10	10	20
Texas B	Texas A&M A	0	0	10	10
Alabama A	Tennessee B	0	0	10	10
Bruin	WashU B	0	10	0	10
Louisville A	Georgia Tech D	0	0	0	0
Louisville B	Kentucky	0	0	0	0
Georgia Tech B	Mississipi State	10	0	10	20
Tennessee A	Sewanee	0	0	10	10
Vanderbilt B	WashU A	0	0	10	10
Bristol	LSE	0	0	10	10
Cambridge B	Imperial A	0	0	10	10
Oxford A	Cambridge C	0	10	10	20
Durham	City St. George's	0	0	10	10
Imperial C	Edinburgh B	0	10	0	10
UCL	Oxford B	0	0	10	10
John Jay	Catholic	0	10	10	20
Columbia A	Maryland A	0	0	10	10
Georgetown	Columbia C	0	0	10	10
Maryland B	Vassar	0	0	10	10
NYU A	Columbia B	0	10	10	20
Johns Hopkins A	NYU B	0	10	10	20
NYU C	Johns Hopkins B	0	0	10	10
Rutgers A	Rutgers B	0	0	0	0
Swarthmore	Maryland C	0	0	10	10
Cornell C	Binghamton A	0	0	10	10
Binghamton B	Rochester	0	0	10	10
Cornell A	Penn State	0	10	10	20
Cornell B	RIT	0	0	10	10
Harvard A	Dartmouth A	0	0	10	10
Dartmouth B	Southern Connecticut State	10	0	10	20